Arthur Apter

Education

Ph.D., Mathematics, Massachusetts Institute of Technology

B.S., Mathematics, Massachusetts Institute of Technology

Journal Articles

(2023). "Normal Measures on Large Cardinals". Transactions of the American Mathematical Society Series B, American Mathematical Society, 10. 129-154.

(2023). "Strong Compactness, Square, GCH, and Woodin Cardinals". Journal of Symbolic Logic,

(2023). "Strong Combinatorial Principles and Level by Level Equivalence". Bollettino dell'Unione Matematica Italiana, Springer-Verlag, 16. 135-150.

Apter, A. (2022). "Controlling the Number of Normal Measures at Successor Cardinals". Mathematical Logic Quarterly, Wiley-Verchag GmbH, 68(3). 304-309.

Apter, A. (2022). "Indestructibility when the First Two Measurable Cardinals are Strongly Compact". Journal of Symbolic Logic, Association for Symbolic Logic, 87(1). 214-227.

(2022). "Indestructibility and the Linearity of the Mitchell Ordering". Archive for Mathematical Logic,

Apter, A., Friedman, S., & Fuchs, G. (2021). "More on HOD-Supercompactness". Annals of Pure and Applied Logic, Elsevier, 172(3). 19 pages.

Apter, A. (2021). "The Ultrapower Axiom UA and the Number of Normal Measures over $\aleph_1$ and $\aleph_2$". Tbilisi Mathematical Journal, Tbilisi Centre for Mathematical Sciences, 14(1). 49-53.

Apter, A., Dimopoulos, S., & Usuba, T. (2021). "Strongly Compact Cardinals and the Continuum Function". Annals of Pure and Applied Logic, Elsevier, 172(9). 12 pages.

Apter, A. (2020). "The Consistency of Level by Level Equivalence with V=HOD, the Ground Axiom, and Instances of Square and Diamond". Bulletin of the Polish Academy of Sciences (Mathematics), Polish Academy of Sciences, 68(1). 1-10.

Apter, A. (2020). "On Weak Square, Approachability, the Tree Property, and Failures of SCH in a Choiceless Context". Mathematical Logic Quarterly, Wiley-Verchag GmbH, 66(1). 115-120.

Apter, A., & Cummings, J. (2019). "Normal Measures on a Tall Cardinal". Journal of Symbolic Logic, The Association for Symbolic Logic, 84(1). 178-204.

Apter, A. (2019). "Tall, Strong, and Strongly Compact Cardinals". Sarajevo Journal of Mathematics, 15(28). 7-22.

Apter, A. (2019). "The Enhanced Levinski Property and the Class of Supercompact Cardinals". Kobe Journal of Mathematics, Kobe University, 36((1-2)). 1-19.

Apter, A. (2018). "Normal Measures and Strongly Compact Cardinals". Bollettino dell'Unione Matematica Italiana, Springer-Verlag, 11(2). 283-292.

Apter, A., Adolf, D. T., & Koepke, P. (2018). "Singularizing Successor Cardinals by Forcing". Proceedings Amer. Math. Soc., American Math. Soc., 146(2). 773-783.

Apter, A. (2017). "A New Easton Theorem for Supercompactness and Level by Level Equivalence". Bull. Polish Acad. Sci., Polish Academy of Sciences, 65(1). 1-10.

Apter, A. (2017). "Precisely Controlling Level by Level Behavior". Math. Logic Quarterly, Wiley-Verlag GmbH, 63(1-2). 77-84.

Apter, A. (2017). "On the Consistency Strength of Level by Level Inequivalence". Arch. for Math. Logic, Springer-Verlag, 56(7-8). 715-723.

Apter, A. (2016). "Indestructibility and Destructible Measurable Cardinals". Arch. for Math. Logic, Springer-Verlag, 55. 3-18.

Apter, A., Dimitriou, I., & Koepke, P. (2016). "All Uncountable Cardinals in the Gitik Model are Almost Ramsey and Carry Rowbottom Filters". Math. Logic Quarterly, Wiley-Verlag GmbH, 62(3). 225-231.

Apter, A. (2016). "Indestructibility and the Levinski Property". Sarajevo Journal of Mathematics, Department of Natural Sciences and Mathematics, Academy of Sciences and Arts of Bosnia and Herzegovina, 12(1). 3-16.

Apter, A. (2016). "A Note on Tall Cardinals and Level by Level Equivalence". Math. Logic Quarterly, Wiley-Verlag GmbH, 62(1). 128-132.

Apter, A. (2015). "Indestructible Strong Compactness and Level by Level Equivalence with No Large Cardinal Restrictions". Bulletin of the Polish Academy of Sciences (Mathematics), Institute of Mathematics, 63. 185-194.

Apter, A. (2015). "A Universal Indestructibility Theorem Compatible with Level by Level Equivalence". Arch. for Math. Logic, Springer-Verlag, 54(3-4). 463-470.

Apter, A. (2015). "Mixed Levels of Indestructibility". Bulletin of the Polish Academy of Sciences (Mathematics), Institute of Mathematics, 63(2). 113-122.

Apter, A. (2014). "Inaccessible Cardinals, Failures of GCH, and Level by Level Equivalence". Notre Dame Journal of Formal Logic, Notre Dame University Press, 55(4). 431-444.

Apter, A. (2014). "Singular Failures of GCH and Level by Level Equivalence". Bull. Polish Academy Sci. (Math.), The Polish Academy of Sciences, 62(1). 11-21.

Apter, A., & Gitik, M. (2014). "On Tall Cardinals and Some Related Generalizations". Israel J. Math., The Magnes Press., 202(1). 343-373.

Apter, A., Koepke, P., & Dimitriou, I. (2014). "The First Measurable Cardinal can be the First Uncountable Regular Cardinal at Any Successor Height" . Math. Logic Quarterly, Wiley-Verlag GmbH, 60(6). 471-486.

Apter, A., & Friedman, S. (2014). "HOD-Supercompactness, Indestructibility, and Level by Level Equivalence". Bulletin of the Polish Academy of Sciences (Mathematics), Institute of Mathematics, 62(3). 197-209.

Apter, A., & Cody, B. (2013). "Consecutive Singular Cardinals and the Continuum Function". Notre Dame Journal of Formal Logic, Notre Dame University Press, 54(2). 125-136.

Apter, A., Jackson, S., & Lowe, B. (2013). "Cofinality and Measurability of the First Three Uncountable Cardinals". Transactions Amer. Math. Soc., The American Mathematical Society, 365(1). 59-98.

Apter, A. (2013). "Indestructible Strong Compactness and Level by Level Inequivalence". Math. Logic Quarterly, Wiley-Verlag GmbH, 59(4-5). 371-377.

Apter, A., Cummings, J., & Hamkins, J. (2013). "Singular Cardinals and Strong Extenders". Central European Journal of Mathematics, Versita and Springer-Verlag, 11(9). 1628-1634.

Apter, A. (2013). "Some Remarks on Tall Cardinals and Failures of GCH". Bulletin of the Polish Academy of Sciences(Mathematics), The Polish Academy of Sciences, Institute of Mathematics, 61(2). 97-106.

(2012). "Indestructibility, Measurability, and Degrees of Supercompactness". Math. Logic Quarterly, Wiley-Verlag GmbH, 58(1-2). 75-82.

(2012). "Indestructible Strong Compactness but not Supercompactness". Annals of Pure and Applied Logic, Elsevier, 163(9). 1237-1242.

(2012). "Inner Models with Large Cardinal Features Usually Obtained by Forcing". Archive for Math. Logic, Springer-Verlag, 51(3-4). 257-283.

(2012). "Level by Level Inequivalence, Strong Compactness, and GCH". Bulletin of the Polish Academy of Sciences (Mathematics), The Polish Academy of Sciences, Institute of Mathematics, 60(3). 201-209.

(2012). "The Wholeness Axioms and the Class of Supercompact Cardinals". Bulletin of the Polish Academy of Sciences (Mathematics), The Polish Academy of Sciences, Institute of Mathematics, 60(2). 101-111.

(2012). "More Easton Theorems for Level by Level Equivalence". Colloquium Mathematicum, The Polish Acadeny of Sciences, Institute of Mathematics, 128(1). 69-86.

(2012). "On Some Questions Concerning Strong Compactness". Archive for Math. Logic, Springer-Verlag, 51(7-8). 819-829.

(2012). "Some Applications of Sargsyan's Equiconsistency Method". Fundamenta Mathematicae, The Polish Academy of Sciences, Institute of Mathematics, 216(3). 207-222.

(2011). "Level by Level Inequivalence beyond Measurability". Archive for Mathematical Logic, Springer-Verlag, 50(7-8). 707-712.

(2011). "A Remark on the Tree Property in a Choiceless Context". Archive for Mathematical Logic, Springer-Verlag, 50(5-6). 585-590.

(2011). "Coding into HOD via Normal Measures with Some Applications". Mathematical Logic Quarterly, Wiley-Verlag GmbH, 57(4). 366-372.

(2011). "Indestructibility, HOD, and the Ground Axiom". Mathematical Logic Quarterly, Wiley-Verlag GmbH, 57(3). 261-265.

(2010). "The Consistency Strength of Choiceless Failures of SCH". Journal of Symbolic Logic, The Association for Symbolic Logic, 75(3). 1066-1080.

(2010). "An Equiconsistency for Universal Indestructibility". Journal of Symbolic Logic, The Association for Symbolic Logic, 75(1). 314-322.

(2010). "How Many Normal Measures Can ¿¿1 +1Carry?". Mathematical Logic Quarterly, Wiley-Verlag GmbH, 56(2). 164-170.

(2010). "Indestructibility, Instances of Strong Compactness, and Level by Level Inequivalence". Archive for Mathematical Logic, Springer-Verlag, 49(7-8). 725-741.

(2010). "Tallness and Level by Level Equivalence and Inequivalence". Mathematical Logic Quaterly, Wiley-Verlag GmbH, 56(1). 4-12.

(2009). "Indestructibility and Stationary Reflection". Mathematical Logic Quarterly, Wiley-Verlag GmbH, 55(3). 228-236.

(2009). "Indestructibility under Adding Cohen Subsets and Level by Level Equivalence". Mathematical Logic Quarterly, Wiley-Verlag GmbH, 55(3). 271-279.

(2009). "Indestructibility, Strong Compactness and Level by Level Equivalence". Fundamenta Mathematicae, The Polish Academy of Sciences, Institute of Mathematics, 204(2). 113-126.

(2009). "L-like Combinatorial Principles and Level by Level Equivalence". Bulletin of the Polish Academy of Sciences (Mathematics), The Polish Academy of Sciences, Institute of Mathematics, 57(3-4). 199-207.

(2009). "Sandwiching the Consistency Strength of Two Global Choiceless Cardinal Patterns". Bulletin of the Polish Academy of Sciences (Mathematics), The Polish Academy of Sciences, Institute of Mathematics, 57(3-4). 189-197.

(2009). "Stationary Reflection and Level by Level Equivalence". Colloquium Mathematicum, The Polish Acadeny of Sciences, Institute of Mathematics, 115(1). 113-128.

(2008). "Indestructibility and Measurable Cardinals with Few and Many Measures". Archive for Mathematical Logic, Springer-Verlag, 47(2). 101-110.

(2008). "An L-like Model Containing Very Large Cardinals". Archive for Math. Logic, Springer-Verlag, 47(1). 65-78.

(2008). "A Note on Indestructibility and Strong Compactness". Bulletin of the Polish Academy of Sciences (Mathematics), The Polish Academy of Sciences, Institute of Mathematics, 56(3-4). 191-197.

(2008). "Making All Cardinals Almost Ramsey". Archive for Mathematical Logic, Springer-Verlag, 47(7-8). 769-783.

(2008). "On the Number of Normal Measures ¿1 and ¿2 can Carry". Tbilisi Mathematical Journal, National Centre for Science and Technology, Tbilisi, Georgia , 1(1). 9-14.

(2008). "Reducing the Consistency Strength of an Indestructibility Theorem". Mathematical Logic Quarterly, Wiley-Verlag GmbH, 54(3). 288-293.

(2008). "Universal Indestructibility for Degrees of Supercompactness and Strongly Compact Cardinals". Archive for Mathematical Logic, Springer-Verlag, 47(2). 133-142.

(2007). "A Reduction in Consistency Strength for Universal Indestructibility". Bulletin of the Polish Academy of Sciences(Mathematics), The Polish Academy of Sciences, Institute of Mathematics, 55(1). 1-6.

(2007). "Indestructibility and Level by Level Equivalence and Inequivalence". Math. Logic Quarterly, Wiley-Verlag GmbH, 53(1). 78-85.

(2007). "Large Cardinals with Few Measures". Proceedings Amer. Math. Soc., The American Mathematical Society, 135(7). 2291-2300.

(2007). "Level by Level Equivalence and the Number of Normal Measures over P¿(¿)". Fundamenta Mathematicae, The Polish Academy of Sciences, Institute of Mathematics, 194(3). 253-265.

(2007). "Supercompactness and Level by Level Equivalence are Compatible with Indestructibility for Strong Compactness". Archive for Math. Logic, Springer-Verlag, 46(3-4). 155-163.

(2006). "Failures of SCH and Level by Level Equivalence". Archive for Math. Logic, Springer-Verlag, 45(7). 831-838.

(2006). "The Least Strongly Compact can be the Least Strong and Indestructible" (the special volume in honor of Jim Baumgartner's 60th birthday). Annals of Pure and Applied Logic, Elsevier, 144(1-3). 33-42.

(2006). "The Consistency Strength of ¿¿ and ¿¿1 being Rowbottom Cardinals without the Axiom of Choice". Archive for Math. Logic, Springer-Verlag, 45(6). 721-737.

(2006). "Supercompactness and Measurable Limits of Strong Cardinals II: Applications to Level by Level Equivalence". Math. Logic Quarterly, Wiley-Verlag GmbH, 52(5). 457-463.

(2006). "Identity Crises and Strong Compactness III: Woodin Cardinals". Archive for Math. Logic, Springer-Verlag, 44(3). 307-322.

(2006). "How Many Normal Measures can ¿¿+1 Carry?". Fundamenta Mathematicae, The Polish Academy of Sciences, Institute of Mathematics, 191(1). 57-66.

(2005). "An Easton Theorem for Level by Level Equivalence". Math. Logic Quarterly, Wiley-Verlag GmbH, 51(3). 247-253.

(2005). "Universal Indestructibility is Consistent with Two Strongly Compact Cardinals". Bulletin of the Polish Academy of Sciences (Mathematics), The Polish Academy of Sciences, Institute of Mathematics, 53(2). 131-135.

(2005). "Removing Laver Functions from Supercompactness Arguments". Math. Logic Quarterly, Wiley-Verlag GmbH, 51(1). 154-156.

(2005). "On a Problem of Foreman and Magidor". Archive for Math. Logic, Springer-Verlag, 44(4). 493-498.

(2005). "Diamond, Square, and Level by Level Equivalence". Archive for Math. Logic, Springer-Verlag, 44(3). 387-395.

(2005). "Can A Large Cardinal Be forced From A Condition Implying Its Negation?". Proceedings Amer. Math. Soc., The American Mathematical Society, 133(10). 3103-3108.

(2005). "Universal Partial Indestructibility and Strong Compactness". Math. Logic Quarterly, Wiley-Verlag GmbH, 51(5). 524-531.

(2004). "Supercompactness and Partial Level by Level Equivalence between Strong Compactness and Strongness". Fundamenta Mathematicae, The Polish Academy of Sciences, Institute of Mathematics, 182(2). 123-136.

(2004). "Level by Level Equivalence and Strong Compactness". Math. Logic Quarterly, Wiley-Verlag GmbH, 50(1). 51-64.

(2004). "Jonsson-like Partition Relations and j : V ¿ V". J. Symbolic Logic, The Association for Symbolic Logic, 69(4). 1267-1281.

(2004). Some Remarks on Indestructibility and Hamkins' Lottery Preparation. Archive for Math. Logic, 50(1). 51-64.

(2003). "Characterizing Strong Compactness via Strongness". Math. Logic Quarterly, Wiley-Verlag GmbH, 49(4). 375-384.

(2003). "Exactly Controlling the Non-Supercompact Strongly Compact Cardinals". J. Symbolic Logic, The Association for Symbolic Logic, 68(2). 669-688.

(2003). "Failures of GCH and the Level by Level Equivalence between Strong Compactness and Supercompactness". Math. Logic Quarterly, Wiley-Verlag GmbH, 49(6). 587-597.

(2003). "Indestructibility, Strongness, and Level by Level Equivalence". Fundamenta Mathematicae, The Polish Academy of Sciences, Institute of Mathematics, 177(1). 45-54.

(2003). "On the Level by Level Equivalence between Strong Compactness and Strongness". Journal of the Mathematical Society of Japan, The Mathematical Society of Japan, 55(1). 47-58.

(2003). "Some Remarks on Indestructibility and Hamkins' Lottery Preparation". Archive for Math. Logic, Springer-Verlag, 42(4). 717-735.

(2002). "Aspects of Strong Compactness, Measurability, and Indestructibility". Archive for Math. Logic, Springer-Verlag, 41(4). 705-719.

(2002). "Blowing up the Power Set of the Least Measurable". J. Symbolic Logic, The Association for Symbolic Logic, 67(3). 915-923.

(2002). "Indestructibility and the Level-by-Level Agreement between Strong Compactness and Supercompactness". J. Symbolic Logic, The Association for Symbolic Logic, 67(2). 820-840.

(2002). "On Level by Level Equivalence and Inequivalence between Strong Compactness and Supercompactness". Fundamenta Mathematicae, The Polish Academy of Sciences, Institute of Mathematics, 171(1). 77-92.

(2002). "On the Non-Extendibility of Strongness and Supercompactness through Strong Compactness". Fundamenta Mathematicae, The Polish Academy of Sciences, Institute of Mathematics, 174(1). 87-96.

(2002). "Strong Cardinals can be Fully Laver Indestructible". Math. Logic Quarterly, Wiley-Verlag GmbH, 48(4). 499-507.

(2001). "Expanding ¿'s Power Set in its Ultrapowers". Radovi Matematicki, The University of Sarajevo, 10(1). 149-156.

(2001). "Identity Crises and Strong Compactness II: Strong Cardinals". Archive for Math. Logic, Springer-Verlag, 40(1). 25-38.

(2001). "Supercompactness and Measurable Limits of Strong Cardinals". J. Symbolic Logic, The Association for Symbolic Logic, 66(2). 629-639.

(2001). "Strong Compactness, Measurability, and the Class of Supercompact Cardinals". Fundamenta Mathematicae, The Polish Academy of Sciences, Institute of Mathematics, 167(1). 65-78.

(2001). "Some Structural Results Concerning Supercompact Cardinals". J. Symbolic Logic, The Association for Symbolic Logic, 66(4). 1919-1927.

(2001). "Some Remarks on Normal Measures and Measurable Cardinals". Math. Logic Quarterly, Wiley-Verlag GmbH, 47(1). 35-44.

(2001). "Some Remarks on a Question of D. H. Fremlin Concerning e-Density". Archive for Math. Logic, Springer-Verlag, 40(4). 531-540.

(2001). "On the Consistency Strength of Two Choiceless Cardinal Patterns". Notre Dame Journal of Formal Logic, Notre Dame University Press, 40(3). 341-345.

(2001). "Indestructible Weakly Compact Cardinals and the Necessity of Supercompactness for Certain Proof Schemata". Math. Logic Quarterly, Wiley-Verlag GmbH, 47(4). 563-571.

(2000). "On a Problem of Woodin". Archive for Math. Logic, Springer-Verlag, 39(4). 253-259.

(2000). "Identity Crises and Strong Compactness". J. Symbolic Logic, The Association for Symbolic Logic, 65(4). 1895-1910.

(2000). "A Note on Strong Compactness and Resurrectibility". Fundamenta Mathematicae, The Polish Academy of Sciences, Institute of Mathematics, 165(3). 285-290.

(2000). "A New Proof of a Theorem of Magidor". Archive for Math. Logic, Springer-Verlag, 39(3). 209-211.

(2000). "A Global Version of a Theorem of Ben-David and Magidor". Annals of Pure and Applied Logic, Elsevier, 102(1). 199-222.

(2000). "Strong Compactness and a Global Version of a Theorem of Ben-David and Magidor". Math. Logic Quarterly, Wiley-Verlag GmbH, 46(4). 453-459.

(2000). "The Calculus of Partition Sequences, Changing Cofinalities, and a Question of Woodin". Transactions Amer. Math. Soc., The American Mathematical Society, 352(3). 969-1003.

(1999). "On Measurable Limits of Compact Cardinals". J. Symbolic Logic, The Association for Symbolic Logic, 64(4). 1675-1688.

(1999). "Forcing the Least Measurable to Violate GCH". Math. Logic Quarterly, Wiley-Verlag GmbH, 45(4). 551-560.

(1999). "Universal Indestructibility". Kobe Journal of Mathematics, Kobe University, 16(2). 119-130.

(1998). "Laver Indestructibility and the Class of Compact Cardinals". J. Symbolic Logic, The Association for Symbolic Logic, 63(1). 149-157.

(1998). "The Least Measurable can be Strongly Compact and Indestructible". J. Symbolic Logic, The Association for Symbolic Logic, 63(1). 1404-1412.

(1997). "More on the Least Strongly Compact Cardinal". Math. Logic Quarterly, Wiley-Verlag GmbH, 43(3). 427-430.

(1997). "Menas' Result is Best Possible". Transactions Amer. Math. Soc., The American Mathematical Society, 349(5). 2007-2034.

(1997). "On the Strong Equality between Supercompactness and Strong Compactness ". Transactions Amer. Math. Soc., The American Mathematical Society, 349(1). 103-128.

(1997). "Patterns of Compact Cardinals". Annals of Pure and Applied Logic, Elsevier, 89(1). 101-115.

(1996). "A Cardinal Pattern Inspired by AD". Math. Logic Quarterly, Wiley-Verlag GmbH, 42(2). 211-218.

(1996). "AD and Patterns of Singular Cardinals below T". J. Symbolic Logic, The Association for Symbolic Logic, 61(1). 225-235.

(1995). "Instances of Dependent Choice and the Measurability of ¿¿+1". Annals of Pure and Applied Logic, Elsevier, 74(3). 203-219.

(1995). "On the First n Strongly Compact Cardinals". Proceedings Amer. Math. Soc., The American Mathematical Society, 123(7). 2229-2235.

(1992). "On Box, Weak Box, and Strong Compactness". Bulletin London Math. Soc., Cambridge University Press, 24(4). 513-518.

(1992). "On the Class of Measurable Cardinals without the Axiom of Choice". Israel J. Math., The Magnes Press, 79(3). 367-379.

(1992). "Some New Upper Bounds in Consistency Strength for Certain Choiceless Large Cardinal Patterns". Archive for Math. Logic, Springer-Verlag, 31(3). 201-205.

(1991). "A Note on Strong Compactness and Supercompactness". Bulletin London Math. Soc., Cambridge University Press, 23(1). 113-115.

(1991). "Relative Consistency Results via Strong Compactness". Fundamenta Mathematicae, The Polish Academy of Sciences, Institute of Mathematics, 139(1). 133-149.

(1990). "Filter Spaces II: Limit Ultraproducts and Iterated Embeddings". Acta Cientifica Venezolano, The Venezuelan Academy of Science, 40(5). 311-318.

(1990). "Successors of Singular Cardinals and Measuarability Revisited". J. Symbolic Logic., The Association for Symbolic Logic, 55(2). 492-501.

(1989). "Filter Spaces: Towards a Unified Theory of Large Cardinal and Embedding Axioms". Annals of Pure and Applied Logic, Elsevier, 41(1). 93-106.

(1988). "On a Problem Inspired by Determinacy". Israel J. Math., The Magnes Press, 61(3). 256-270.

(1988). "Some Results on Specker's Problem". Pacific J. Math., The Pacific Journal of Mathematics at the University of California, Berkeley, 134(2). 227-249.

(1986). "Large Cardinal Structures below ¿¿". J. Symbolic Logic., The Association for Symbolic Logic, 51(3). 591-603.

(1985). "A Cardinal Structure Theorem for an Ultrapower". Canadian Mathematical Bulletin, The University of Toronto Press, 28(4). 472-473.

(1985). "An AD-Like Model". J. Symbolic Logic., The Association for Symbolic Logic, 50(2). 531-543.

(1985). "Successors of Singular Cardinals and Measurability". Advances in Mathematics, Academic Press, 55(3). 228-241.

(1985). "Some Results on Consecutive Large Cardinals II: Applications of Radin Forcing". Israel J. Math., The Magnes Press, 52(4). 273-292.

(1984). "A Generalized Version of the Singular Cardinals Problem". Fundamenta Mathematicae, The Polish Academy of Sciences, Institute of Mathematics, 121(2). 99-116.

(1983). "On a Problem of Silver". Fundamenta Mathematicae, The Polish Academy of Sciences, Institute of Mathematics, 116(1). 33-38.

(1983). "Some Results on Consecutive Large Cardinals". Annals of Pure and Applied Logic, Elsevier, 25(1). 1-17.

(1981). "Measurability and Degrees of Strong Compactness". J. Symbolic Logic., The Association for Symbolic Logic, 46(2). 180-185.

(1981). "Changing Cofinalitites and Infinite Exponents". J. Symbolic Logic., The Association for Symbolic Logic, 46(1). 89-95.

(1980). "On The Least Strongly Compact Cardinal". Israel J. Math., The Magnes Press, 35(3). 225-233.

"Indestructible Supercompactness and Level by Level Inequivalence". Annals of Pure and Applied Logic,

"A Remark on a Question of Woodin". In Progress.

"Gap Forcing, Level by Level Equivalence, and an Application". In Progress.

Book Chapters

Apter, A. (2019). "Global Failures of GCH, Level by Level Equivalence, V=HOD, and the Ground Axiom". Research Trends in Contemporary Logic

Presentations

Apter, A. (2024, July 8). Virtual participant. Advances in Set Theory 2022. Jerusalem, Israel: Hebrew University.

Apter, A., & Cummings, J. (2022, March 12). "Normal Measures and Measurable Cardinals". Special Session on Large Cardinals and Forcing Axioms (cancelled due to the pandemic). University of Virginia, Charlottesville, Virginia: American Mathematical Society.

Apter, A. (2024, October 8). Invited participant, Luminy Set Theory Conference (participated virtually). 16th International Workshop on Set Theory. Luminy (Marseille), France: CIRM.

Apter, A. (2020, September 18). "UA and the Number of Normal Measures over $\aleph_{\omega + 1}$". CUNY Virtual Set Theory Seminar. Online (Virtual): CUNY.

Apter, A. (2020, April 24). "Indestructibility and the First Two Strongly Compact Cardinals". CUNY Virtual Set Theory Seminar. Online (Virtual): CUNY.

Apter, A. (2019, October 8). "Indestructibility and the First Two Strongly Compact Cardinals". Carnegie Mellon University Logic Seminar. Carnegie Mellon University: Department of Mathematics, Carnegie Mellon University.

Apter, A. (2019, May 21). Contributed Talks, Session I. Chaired, Association for Symbolic Logic (ASL) 2019 North American Annual Meeting. CUNY Graduate Center: Association for Symbolic Logic.

Apter, A. (2018, January 10). "Strong Compactness, Easton Functions, and Indestructibility". First Mexico-USA Logic Fest. Mexico City, Mexico: ITAM.

Apter, A. (2017, October 9). "Tall, Strong, and Strongly Compact Cardinals". 14th International Workshop on Set Theory. Luminy (Marseille), France: CIRM.

Apter, A., & Gitik, M. (2016, February 17). "The Measurable and Tall Cardinals can Coincide on a Proper Class". Menachem Magidor 70th Birthday Conference. Jerusalem, Israel: Department of Mathematics, Hebrew University.

Apter, A. (2015, December 31). Logic Seminar, Logic Workshop, Set Theory Seminar. Presented Talk (1977 - 2016). : Mathematics Department of Carnegie Mellon Unversity, CUNY, Dartmouth College, Hebrew University, MIT, and Rutgers University.

Apter, A., & Cummings, J. (2015, November 30). "Normal Measures and Tall Cardinals". Independence Results in Mathematics and Challenges in Iterated Forcing. University of East Anglia, Norwich, England

Apter, A. (2014, May 24). "Namba-like Forcings at Successors of Singular Cardinals". Infinity, Computability, and Metamathematics: Conference in honor of the 60th birthdays of Peter Koepke and Philip Welch. Bonn, Germany

Apter, A. (2014, March 31). Conference held in honor of the 60th birthday of Philip Welch. Chaired (lecture presented by Peter Koepke). : University of Bristol.

Apter, A. (2014, March 4). "Normal Measures and Strongly Compact Cardinals". INFTY Final Conference. Bonn, Germany

Apter, A. (2012, April 7). Appalachian Set Theory Workshop. Supported Participant. Cornell University

Apter, A. (2011, March 19). Appalachian Set Theory Workshop. Participant. Carnegie Mellon University

Apter, A. (2011, January 31). Set Theory. Invited Participant. Oberwolfach, Germany: Mathematics Research Institute.

Apter, A. (2011, January 17). Oberseminar in Logic. Invited Seminar Speaker. : Rheinische Freidrich-Wilhelms- University.

Apter, A. (2010, April 3). Appalachian Set Theory Workshop. Participant. : Carnegie Mellon University.

Apter, A. (2010, February 28). MAMLS in honor of Richard Laver. Invited Speaker. : University of Colorado, Boulder.

Apter, A. (2009, June 30). ESI Workshop on Large Cardinals and Descriptive Set Theory. Invited and Supported Speaker. Vienna, Austria: Erwin Schrodinger Institute.

Apter, A. (2009, June 30). Infinitary Combinatorics without the Axiom of Choice (ICWAC). Invited Speaker. Bonn, Germany: Rheinische Freidrich-Wilhelms- University.

Apter, A. (2009, February 28). Very Informal Gathering in honor of the 60th birthday of Professor John Steel of the University of California, Berkeley. Participant. : UCLA.

Apter, A. (2009, May 11). Oberseminar in Logic. Invited Seminar Speaker. : Rheinische Freidrich-Wilhelms- University.

Apter, A., Koepke, P., Lowe, B., & Dimitriou, I. (2009, June 30). Infinitary Combinatorics without the Axiom of Choice (ICWAC). Program Organizer. Bonn, Germany: Rheinische Freidrich-Wilhelms- University.

Apter, A. (2009, May 31). Amsterdam Workshop in Set Theory. Invited Speaker. Amsterdam, The Netherlands: University of Amsterdam.

Apter, A. (2008, April 17). Oberseminar in Logic. Invited Seminar Speaker. : Rheinische Freidrich-Wilhelms- University.

Apter, A. (2008, April 23). Oberseminar in Logic. Invited Seminar Speaker. : University of Munster.

Apter, A. (2008, March 31). Annual Meeting of the Association for Symbolic Logic. Participant. : University of California, Irvine.

Apter, A. (2007, May 25). Oberseminar in Logic. Invited Seminar Speaker. : University of Munster.

Apter, A. (2007, March 31). Annual Meeting of the Association for Symbolic Logic. Participant. : University of Florida, Gainesville.

Apter, A. (2007, March 31). Workshop on Singular Cardinal Combinatorics and Inner Model Theory. Supported Participant. : University of Florida, Gainesville.

Apter, A. (2007, March 31). The Special Session on Large Cardinals in Set Theory. Participant. Miami University, Oxford, Ohio: The Sectional Meeting of the American Mathematical Society.

Apter, A., Cummings, J., & Foreman, M. (2006, February 28). Mid-Atlantic Mathematical Logic Seminar (MAMLS) in honor of the 60th birthday of Professor Menachem Magidor of Hebrew University. Program Organizer. Irvine, CA: University of California-Irvine.

Apter, A. (2006, September 9). Inaugural Appalachian Set Theory Workshop. Supported Participant. : Carnegie Mellon University.

Apter, A. (2005, January 31). Oberseminar in Logic. Invited Seminar Speaker. : University of Munster.

Apter, A. (2005, January 18). Oberseminar in Logic. Invited Seminar Speaker. : Rheinsche Friedrich-Wilhems-University.

Apter, A. (2004, May 31). Annual Meeting of the Association for Symbolic Logic. Chaired (Special Session). : Carnegie Mellon University.

Apter, A. (2003, August 31). Special Session on Set Theory, European Summer Meeting of the Association for Symbolic Logic (Logic Colloquium '03). Invited Speaker. Helsinki, Finland: Association for Symbolic Logic.

Apter, A., & Groszek, M. (2003, October 31). Mid-Atlantic Mathematical Logic Seminar in honor of the 60th birthday of Professor James Baumgartner of Dartmouth College. Program Organizer and Invited Speaker. : Dartmouth College.

Apter, A. (2003, January 31). Winter Meeting of the Association for Symbolic Logic ( with Joint Mathematics Meetings). Invited Speaker. Baltimore, MD: Association for Symbolic Logic.

Apter, A. (2002, May 31). Logic Seminar. Invited speaker. : Penn State University.

Apter, A. (2002, January 31). Set Theory. Invited Participant and Speaker at the "by invitation only" meeting in Mengenlehre. Oberwolfach, Germany: Mathematics Research Institute.

Apter, A. (2001, May 31). International Conference on Logic and Algebra. Invited Speaker. Istanbul, Turkey: Istanbul Bilgi University.

Apter, A. (2001, March 31). Annual Meeting of the Association for Symbolic Logic. Participant. : University of Pennsylvania.

Apter, A. (2001, January 31). Informal Meeting in Set Theory. Scheduled Speaker (unable to attend). Bonn, Germany: Rheinische Freidrich-Wilhelms-University.

Apter, A. (2000, May 31). Mid-Atlantic Mathematical Logic Seminar. Invited Speaker. : University of Maryland.

Apter, A. (2000, March 31). . Invited Colloquium and Seminar Speaker in Europe at the University of East Anglia, Norwich, England, Rheinsche Friedrich-Wilhelms-University, Bonn, Germany, and the University of Vienna, Vienna, Austria.

Apter, A. (1999, August 31). International Conference on Topology and its Applications. Invited Speaker. Yokohama, Japan: Kanagawa University.

Apter, A. (1999, September 30). . Invited colloquium and seminar speaker in Japan at Kobe University, Nagoya University, Tsukuba University, and Waseda University.

Apter, A. (1999, May 31). The Biennial MIT Logic Conference. Supported Participant. : MIT.

Apter, A. (1999, January 31). Workshop in Set Theory. Participant. Norwich, England: University of East Anglia.

Apter, A. (1999, January 11). . Invited Colloquium Speaker, University of East Anglia Pure Mathematics Colloquium.

Apter, A. (1999, January 7). Set Theory, Analysis, and their Neighbours (STAATN) Meeting. Invited Speaker. London, England: London Mathematical Society.

Apter, A., & Kirby, L. (1998, February 28). the Mid-Atlantic Mathematical Logic Seminar. Co-Organizer and Co-Chair. New York, NY: Baruch College.

Apter, A. (1997, March 31). Annual Meeting of the Association for Symbolic Logic. Participant. : MIT.

Apter, A. (1997, January 31). Annual Meeting of the American Mathematical Society. Participant. San Diego, California

Apter, A. (1996, January 31). Set Theory. Invited Participant and Speaker at the "by invitation only" meeting in Mengenlehre. Oberwolfach, Germany: Mathematics Research Institute.

Apter, A. (1995, August 31). The European Summer Meeting of the Association for Symbolic Logic. Participant. The Technion, Haifa, Israel: Haifa University.

Apter, A., & Kirby, L. (1995, December 31). the Mid-Atlantic Mathematical Logic Seminar. Co-Organizer and Co-Chair. New York, NY: Baruch College.

Apter, A. (1995, May 31). The Biennial MIT Logic Conference. Participant. : MIT.

Apter, A. (1995, January 31). Logic Colloquium. Invited Colloquium Speaker. : UCLA.

Apter, A., & Kirby, L. (1994, February 28). the Mid-Atlantic Mathematical Logic Seminar. Co-Organizer and Co-Chair. New York, NY: Baruch College.

Apter, A. (1993, May 31). Special Session devoted primarily to Set Theory at the Sacks Symposium. Chaired. : MIT.

Apter, A. (1993, April 30). . Invited Colloquium Speaker, Carnegie Mellon University Mathematics Department Colloquium.

Apter, A. (1992, November 30). . Invited Colloquium Speaker, Tel-Aviv University Mathematics Department Colloquium.

Apter, A. (1992, December 31). . Invited Colloquium Speaker, Haifa University Mathematics Department Colloquium.

Apter, A. (1992, April 30). The Special Session in Set Theory of the meeting of the American Mathematical Society. Presented a Contributed Talk. : Lehigh University.

Apter, A., & Kirby, L. (1990, December 31). the Mid-Atlantic Mathematical Logic Seminar. Co-Organizer and Co-Chair. New York, NY: Baruch College.

Apter, A. (1990, August 31). . Invited Visitor. : Tel-Aviv University.

Apter, A. (1990, July 31). . Offered Membership. Berkeley, California: Mathematical Sciences Research Institute (MSRI).

Apter, A. (1989, October 31). Set Theory and Continuum Conference. Invited and Supported Participant. Berkeley, California: Mathematical Sciences Research Institute (MSRI).

Apter, A. (1989, April 30). The Biennial MIT Logic Conference. Participant. : MIT.

Apter, A. (1988, May 31). The Union College Set Theory Conference. Participant. Schenectady, New York

Apter, A. (1988, February 28). the Mid-Atlantic Mathematical Logic Seminar. Organized and Chaired. : Baruch College.

Apter, A. (1987, December 31). Session held in honor of John Myhill at the Annual Meeting of the Association for Symbolic Logic. Participant. New York City

Apter, A. (1987, August 31). Logic Conference. Invited Speaker (unable to attend). Kyoto, Japan: Research Institute for Mathematical Sciences of Kyoto University.

Apter, A. (1987, May 31). Meeting of The Association for Symbolic Logic. Participant. New York, New York: Courant Institute of Mathematical Sciences.

Apter, A. (1986, August 31). International Congress of Mathematicians. Participant. Berkeley, California

Apter, A. (1986, January 31). Annual Meeting of the Association for Symbolic Logic. Participant. New Orleans, Louisiana

Apter, A. (1985, July 31). . Invited Visitor. : Tel-Aviv University.

Apter, A. (1985, July 31). The European Summer Meeting of the Association for Symbolic Logic. Participant. : University of Paris South, France.

Apter, A. (1985, April 30). The Biennial MIT Logic Conference. Participant. : MIT.

Apter, A. (1984, July 31). The European Summer Meeting of the Association for Symbolic Logic. Participant. : University of Manchester, England.

Apter, A. (1984, May 31). The Union College Set Theory Conference. Presented a Contributed Talk. Schenectady, NY

Apter, A. (1983, December 31). Annual Meeting of the Association for Symbolic Logic. Participant. Boston, Massachusetts

Apter, A. (1983, June 30). American Mathematical Society Summer Research Conference in Set Theory. Invited and Supported Participant. : University of Colorado, Boulder.

Apter, A. (1983, April 30). The Biennial MIT Logic Conference. Participant. : MIT.

Apter, A. (1983, April 30). . Invited Colloquium Speaker, SUNY Buffalo Logic Colloquium.

Apter, A. (1982, July 31). American Mathematical Society Summer Institute in Recursion Theory. Invited and Supported Participant. : Cornell University.

Apter, A. (1981, October 31). The American Mathematical Society Meeting. Participant. : University of Massachusetts.

Apter, A. (1981, April 30). The Biennial MIT Logic Conference. Participant. : MIT.

Apter, A. (1981, January 31). The Annual Meeting of the Association for Symbolic Logic. Presented a Contributed Talk. San Francisco, CA

Apter, A. (1980, March 31). . Invited Speaker, IVIC. Caracas, Venezuela

Apter, A. (1979, May 31). The Union College Set Theory Conference. Presented a Contributed Talk. Schenectady, NY

Apter, A. (1979, January 31). Logic Colloquium. Presented a Colloquium Talk. : UCLA.

Apter, A. (1979, January 31). . Presented a Seminar Talk at the University of California-Berkeley.

Apter, A. (1978, August 31). NATO Summer School in Set Theory. Invited and Supported Participant. : Cambridge University, England.

Apter, A. (1978, June 30). Kleene Symposium. Participant. : University of Wisconsin, Madison.

Reviews

Apter, A. (2002,January 1). Review of three papers by Cummings and one paper by Foreman, Cummings, and Magidor. Bull. Symbolic Logic.

Apter, A. (2001,January 1). Review of papers by Abraham, Cummings, and Foreman, and Magidor and Shelah on the Tree Property. Bull. Symbolic Logic.

Research Currently in Progess

Apter, A.(n.d.). Indestructbility and Fast Functions. In Progress.

Apter, A.(n.d.). Indestructibility and a Construction of Cummings. In Progress.

Apter, A.(n.d.). Indestructibility and a Question of Schindler. In Progress.

Apter, A.(n.d.). Indestructibility and GCH at Measurable Cardinals. In Progress.

Apter, A.(n.d.). Indestructibility and HOD Supercompactness. In Progress.

Apter, A.(n.d.). Indestructibility and Instances of the Tree Property. In Progress.

Apter, A.(n.d.). Indestructibility for Strong Cardinals and Level by Level Inequivalence. In Progress.

Apter, A.(n.d.). Indestructibility for Strong Compactness with a Bit of Supercompactness. In Progress.

Apter, A.(n.d.). Indestructibility under Adding Non-Reflecting Stationary Sets, Failures of GCH, and Partial Supercompactness. In Progress.

Apter, A.(n.d.). Indestructibility under Prikry Iterations, Level by Level Equivalence, and Strongness. In Progress.

Apter, A.(n.d.). Indestructibility under Sacks Forcing and Level by Level Equivalence. In Progress.

Apter, A.(n.d.). Instances of Dependent Choice, Successors of Singular Cardinals, and Measurability: Countable Cofinality. In Progress.

Apter, A., & Magidor, M.(n.d.). Instances of Dependent Choice, Successors of Singular Cardinals, and Measurability: Uncountable Cofinality. In Progress.

Apter, A.(n.d.). Level by Level Equivalence and Fast Functions. In Progress.

Apter, A.(n.d.). Level by Level Equivalence and Fragile Measurability. In Progress.

Apter, A.(n.d.). Level by Level Equivalence and Instances of the Tree Property. In Progress.

Apter, A.(n.d.). Level by Level Equivalence and the Nonstationary Ideal. In Progress.

Apter, A.(n.d.). Level by Level Inequivalence and the Levinski Property. In Progress.

Apter, A., Friedman, S., Gitik, M., & Magidor, M.(n.d.). Making HOD and V Agree on Cardinals but Disagree on Cofinalities. In Progress.

Apter, A.(n.d.). Menas' Result Remains Best Possible in a Generalized Context. In Progress.

Apter, A.(n.d.). More Failures of GCH and Level by Level Equivalence. In Progress.

Apter, A.(n.d.). More on the Class of Measurable Cardinals without the Axiom of Choice. In Progress.

Apter, A.(n.d.). Namba-like Forcings at Successors of Singular Cardinals from Strong Compactness. In Progress.

Apter, A.(n.d.). Normal Measures Concentrating on Singular Ordinals. In Progress.

Apter, A.(n.d.). Normal Measures in V versus HOD. In Progress.

Apter, A.(n.d.). On Large Cardinals in a Choiceless Context. In Progress.

Apter, A.(n.d.). On Level by Level Inequivalence between Strong Compactness and Strongness. In Progress.

Apter, A.(n.d.). On Strong Compactness, Strongness, and their Possible Interactions. In Progress.

Apter, A.(n.d.). A Model with a Namba-like Forcing at the Successor of Every Singular Cardinal. In Progress.

Apter, A.(n.d.). A New Upper Bound in Consistency Strength for a Choiceless Large Cardinal Pattern. In Progress.

Apter, A.(n.d.). Adding Cohen Subsets, Indestructibility, Level by Level Equivalence, and Strongness. In Progress.

Apter, A.(n.d.). Additional Failures of SCH with Level by Level Equivalence. In Progress.

Apter, A.(n.d.). An Alternate Forcing Proof of the Relative Consistency of Two Consecutive Measurable Cardinals. In Progress.

Apter, A.(n.d.). An Easton Theorem for Strong Compactness and Supercompactness. In Progress.

Apter, A.(n.d.). An Identity Crisis for Partial Supercompactness. In Progress.

Apter, A.(n.d.). Blocks of Alternating Level by Level Equivalence and Inequivalence. In Progress.

Apter, A.(n.d.). Changing the Degree of Supercompactness of the Least Measurable Limit of Compact Cardinals. In Progress.

Apter, A.(n.d.). Choiceless Cardinal Patterns using Strong Compactness. In Progress.

Apter, A., Lowe, B., Jackson, S., & Blass, A.(n.d.). Cofinality Patterns Below ¿¿. In Progress.

Apter, A.(n.d.). Collapsing HOD Cardinals via Strong Compactness. In Progress.

Apter, A.(n.d.). Controlling Level by Level Equivalence Locally. In Progress.

Apter, A., & Cummings, J.(n.d.). Correct Cardinals. In Progress.

Apter, A.(n.d.). Destroying and Resurrecting Level by Level Equivalence. In Progress.

Apter, A.(n.d.). Exact Control with Final Segments of Level by Level Equivalence and Inequivalence. In Progress.

Apter, A., Cummings, J., & Gitik, M.(n.d.). Extending Hamkins' Gap Forcing Results to Prikry Iterations. In Progress.

Apter, A.(n.d.). GCH and the Least Measurable Limit of Compact Cardinals. In Progress.

Apter, A.(n.d.). Identity Crises and Strong Compactness V: Strongly Unfoldable Cardinals. In Progress.

Apter, A., & Friedman, S.(n.d.). Identity Crises and Strong Compactness VI: HOD Supercompactness. In Progress.

Apter, A.(n.d.). On Strong Compactness, Supercompactness, and Squares. In Progress.

Apter, A.(n.d.). On the Classes of Tall, Strong, Strongly Compact, and Supercompact Cardinals. In Progress.

Apter, A.(n.d.). On the Non-Extendibility of Strong Unfoldability through Strong Compactness and Tallness. In Progress.

Apter, A., & Koepke, P.(n.d.). On the T-Function in a Choiceless Context. In Progress.

Apter, A.(n.d.). Patterns of Indestructible Compact Cardinals. In Progress.

Apter, A.(n.d.). Reducing the Consistency Strength of Some Choiceless Large Cardinal Patterns. In Progress.

Apter, A.(n.d.). Removing Laver Functions from Strongness Arguments. In Progress.

Apter, A.(n.d.). Resurrectibility and Level by Level Equivalence. In Progress.

Apter, A., & Cody, B.(n.d.). Reverse Easton Iterations and Nontrivial Elementary Embeddings from V to V. In Progress.

Apter, A.(n.d.). Some Indestructibility Theorems using Shelah Type Partial Orderings. In Progress.

Apter, A., & Magidor, M.(n.d.). Some Remarks on the Values of the Cofinality Function in a Model of ZF. In Progress.

Apter, A.(n.d.). Some Results on Strong Compactness, Supercompactness, and Failures of GCH. In Progress.

Apter, A.(n.d.). Some Structural Results Concerning Hypercompact Cardinals. In Progress.

Apter, A., & Cummings, J.(n.d.). Strong Cardinals and Normal Measures of Trivial Mitchell Order. In Progress.

Apter, A., Habic, M., & Honzik, R.(n.d.). Tall Cardinals and Capturing. In Progress.

Apter, A.(n.d.). The Consistency of V=HOD with Level by Level Inequivalence. In Progress.

Apter, A., & Koepke, P.(n.d.). The First Jonsson Cardinal can be Singular. In Progress.

Apter, A.(n.d.). Uniform Levels of Indestructibility. In Progress.

Apter, A.(n.d.). Universal Indestructibility and Level by Level Equivalence. In Progress.

Apter, A.(n.d.). Universal Indestructibility and Sacks Forcing. In Progress.

Apter, A.(n.d.). V=HOD and Failures of Level by Level Equivalence. In Progress.

Apter, A., & Hamkins, J.(n.d.). V=HOD and the Class of Compact Cardinals. In Progress.

Apter, A.(n.d.). V=HOD, Normal Measures, and the Class of Supercompact Cardinals. In Progress.

College

University

Public