Distinguished Professor of Mathematics

Baruch College of CUNY

The CUNY Graduate Center

B.S.,
Mathematics,
M.I.T.,
1975.

Ph.D.,
Mathematics,
M.I.T.,
1978.

Mathematical Logic, specifically Set Theory: Large Cardinals and Forcing.

Joel Hamkins, whom I thank for helping me to set up this web page, has created a page containing links of interest to logicians both in the greater New York area and elsewhere. Click here to access these links. Click here to find out information about MAMLS.

- "On the Least Strongly Compact Cardinal", Israel Journal of Mathematics 35, 1980, 225-233.
- "Changing Cofinalities and Infinite Exponents", Journal of Symbolic Logic 46, 1981, 89-95.
- "Measurability and Degrees of Strong Compactness", Journal of Symbolic Logic 46, 1981, 180-185.
- "On a Problem of Silver", Fundamenta Mathematicae 116, 1983, 33-38.
- "Some Results on Consecutive Large Cardinals", Annals of Pure and Applied Logic 25, 1983, 1-17.
- "A Generalized Version of the Singular Cardinals Problem", Fundamenta Mathematicae 121, 1984, 99-116.
- "Successors of Singular Cardinals and Measurability", Advances in Mathematics 55, 1985, 228-241.
- "An AD-Like Model", Journal of Symbolic Logic 50, 1985, 531-543.
- "A Cardinal Structure Theorem for an Ultrapower", Canadian Mathematical Bulletin 28, 1985, 472-473.
- "Some Results on Consecutive Large Cardinals II: Applications of Radin Forcing", Israel Journal of Mathematics 52, 1985, 273-292.
- (with J. Henle) "Large Cardinal Structures Below $\aleph_\omega$", Journal of Symbolic Logic 51, 1986, 591-603.
- "On a Problem Inspired by Determinacy", Israel Journal of Mathematics 61, 1988, 256-270.
- (with M. Gitik) "Some Results on Specker's Problem", Pacific Journal of Mathematics 134, 1988, 227-249.
- (with C. DiPrisco, J. Henle, and W. Zwicker) "Filter Spaces: Towards a Unified Theory of Large Cardinal and Embedding Axioms", Annals of Pure and Applied Logic 41, 1989, 93-106.
- "Successors of Singular Cardinals and Measurability Revisited", Journal of Symbolic Logic 55, 1990, 492-501.
- (with C. DiPrisco, J. Henle, and W. Zwicker) "Filter Spaces II: Limit Ultraproducts and Iterated Embeddings", Acta Cientifica Venezolano 40, 1990, 311-318.
- "A Note on Strong Compactness and Supercompactness", Bulletin of the London Mathematical Society 23, 1991, 113-115.
- (with J. Henle) "Relative Consistency Results via Strong Compactness", Fundamenta Mathematicae 139, 1991, 133-149.
- "Some New Upper Bounds in Consistency Strength for Certain Choiceless Large Cardinal Patterns", Archive for Mathematical Logic 31, 1992, 201-205. .dvi file, Plain TeX file.
- (with J. Henle) "On Box, Weak Box, and Strong Compactness", Bulletin of the London Mathematical Society 24, 1992, 513-518. .dvi file, Plain TeX file.
- "On the Class of Measurable Cardinals Without the Axiom of Choice", Israel Journal of Mathematics 79, 1992, 367-379. .dvi file, Plain TeX file.
- "On the First n Strongly Compact Cardinals", Proceedings of the American Mathematical Society 123, 1995, 2229-2235. .dvi file, Plain TeX file.
- (with M. Magidor) "Instances of Dependent Choice and the Measurability of $\aleph_{\omega + 1}$", Annals of Pure and Applied Logic 74, 1995, 203-219. .dvi file, Plain TeX file.
- "AD and Patterns of Singular Cardinals below $\Theta$", Journal of Symbolic Logic 61, 1996, 225-235. .dvi file, Plain TeX file.
- "A Cardinal Pattern Inspired by AD", Mathematical Logic Quarterly 42, 1996, 211-218. .dvi file, Plain TeX file.
- (with S. Shelah) "On the Strong Equality between Supercompactness and Strong Compactness", Transactions of the American Mathematical Society 349, 1997, 103-128. .dvi file, Plain TeX file.
- (with S. Shelah) "Menas' Result is Best Possible", Transactions of the American Mathematical Society 349, 1997, 2007-2034. .dvi file, Plain TeX file.
- "More on the Least Strongly Compact Cardinal", Mathematical Logic Quarterly 43, 1997, 427-430. .dvi file, Plain TeX file.
- "Patterns of Compact Cardinals", Annals of Pure and Applied Logic 89, 1997, 101-115. .dvi file, Plain TeX file.
- "Laver Indestructibility and the Class of Compact Cardinals", Journal of Symbolic Logic 63, 1998, 149-157. .dvi file, Plain TeX file.
- (with M. Gitik) "The Least Measurable can be Strongly Compact and Indestructible", Journal of Symbolic Logic 63, 1998, 1404-1412. .dvi file, Plain TeX file.
- "Forcing the Least Measurable to Violate GCH", Mathematical Logic Quarterly 45, 1999, 551-560. .dvi file, LaTeX file.
- "On Measurable Limits of Compact Cardinals", Journal of Symbolic Logic 64, 1999, 1675-1688. .dvi file, Plain TeX file.
- (with J. D. Hamkins) "Universal Indestructibility", Kobe Journal of Mathematics 16, 1999, 119-130. .dvi file, Plain TeX file.
- (with J. Henle and S. Jackson) "The Calculus of Partition Sequences, Changing Cofinalities, and a Question of Woodin", Transactions of the American Mathematical Society 352, 2000, 969-1003. .dvi file, LaTeX file.
- (with J. Cummings) "A Global Version of a Theorem of Ben-David and Magidor", Annals of Pure and Applied Logic 102, 2000, 199-222. .dvi file, LaTeX file.
- "A New Proof of a Theorem of Magidor", Archive for Mathematical Logic 39, 2000, 209-211. .dvi file, Plain TeX file.
- "On a Problem of Woodin", Archive for Mathematical Logic 39, 2000, 253-259. .dvi file, Plain TeX file.
- "Strong Compactness and a Global Version of a Theorem of Ben-David and Magidor", Mathematical Logic Quarterly 46, 2000, 453-459. .dvi file, LaTeX file.
- (with J. Cummings) "Identity Crises and Strong Compactness", Journal of Symbolic Logic 65, 2000, 1895-1910. .dvi file, Plain TeX file.
- "A Note on Strong Compactness and Resurrectibility", Fundamenta Mathematicae 165, 2000, 285-290. .dvi file, LaTeX file.
- (with J. Cummings) "Identity Crises and Strong Compactness II: Strong Cardinals", Archive for Mathematical Logic 40, 2001, 25-38. .dvi file.
- "Some Remarks on Normal Measures and Measurable Cardinals", Mathematical Logic Quarterly 47, 2001, 35-44. .dvi file, LaTeX file.
- "Strong Compactness, Measurability, and the Class of Supercompact Cardinals", Fundamenta Mathematicae 167, 2001, 65-78. .dvi file, LaTeX file.
- "Supercompactness and Measurable Limits of Strong Cardinals", Journal of Symbolic Logic 66, 2001, 629-639. .dvi file, LaTeX file.
- "On the Consistency Strength of Two Choiceless Cardinal Patterns", Notre Dame Journal of Formal Logic 40, 1999, 341-345. Note: This paper actually appeared during the summer of 2001. .dvi file, LaTeX file.
- (with M. Dzamonja) "Some Remarks on a Question of D. H. Fremlin Regarding $\epsilon$-Density", Archive for Mathematical Logic 40, 2001, 531-540. .dvi file, LaTeX file.
- (with J. D. Hamkins) "Indestructible Weakly Compact Cardinals and the Necessity of Supercompactness for Certain Proof Schemata", Mathematical Logic Quarterly 47, 2001, 563-571. .dvi file, LaTeX file.
- "Expanding $\kappa$'s Power Set in its Ultrapowers", Radovi Matematicki 10, 2001, 149-156. .dvi file, LaTeX file.
- "Some Structural Results Concerning Supercompact Cardinals", Journal of Symbolic Logic 66, 2001, 1919-1927. .dvi file, LaTeX file.
- "On Level by Level Equivalence and Inequivalence between Strong Compactness and Supercompactness", Fundamenta Mathematicae 171, 2002, 77-92. .dvi file, LaTeX file.
- (with J. D. Hamkins) "Indestructibility and the Level-by-Level Agreement between Strong Compactness and Supercompactness", Journal of Symbolic Logic 67, 2002, 820-840. .dvi file.
- (with J. Cummings) "Blowing up the Power Set of the Least Measurable", Journal of Symbolic Logic 67, 2002, 915-923. .dvi file.
- "On the Non-Extendibility of Strongness and Supercompactness through Strong Compactness", Fundamenta Mathematicae 174, 2002, 87-96. .dvi file.
- "Strong Cardinals can be Fully Laver Indestructible", Mathematical Logic Quarterly 48, 2002, 499-507. .dvi file, LaTeX file.
- "Aspects of Strong Compactness, Measurability, and Indestructibility", Archive for Mathematical Logic 41, 2002, 705-719. .dvi file, LaTeX file.
- "On the Level by Level Equivalence between Strong Compactness and Strongness", Journal of the Mathematical Society of Japan 55, 2003, 47-58. .dvi file.
- (with J. D. Hamkins) "Exactly Controlling the Non-Supercompact Strongly Compact Cardinals", Journal of Symbolic Logic 68, 2003, 669-688. .dvi file, LaTeX file.
- "Characterizing Strong Compactness via Strongness", Mathematical Logic Quarterly 49, 2003, 375-384. .dvi file, LaTeX file.
- "Failures of GCH and the Level by Level Equivalence between Strong Compactness and Supercompactness", Mathematical Logic Quarterly 49, 2003, 587-597. .dvi file, LaTeX file.
- "Indestructibility, Strongness, and Level by Level Equivalence", Fundamenta Mathematicae 177, 2003, 45-54. .dvi file, LaTeX file.
- "Some Remarks on Indestructibility and Hamkins' Lottery Preparation", Archive for Mathematical Logic 42, 2003, 717-735. .dvi file, LaTeX file.
- "Level by Level Equivalence and Strong Compactness", Mathematical Logic Quarterly 50, 2004, 51-64. .dvi file, LaTeX file.
- "Supercompactness and Partial Level by Level Equivalence between Strong Compactness and Strongness", Fundamenta Mathematicae 182, 2004, 123-136. .dvi file, LaTeX file.
- (with G. Sargsyan) "Jonsson-like Partition Relations and j : V ---> V", Journal of Symbolic Logic 69, 2004, 1267-1281. .dvi file, LaTeX file.
- "Removing Laver Functions from Supercompactness Arguments", Mathematical Logic Quarterly 51, 2005, 154-156. .dvi file, LaTeX file.
- "An Easton Theorem for Level by Level Equivalence", Mathematical Logic Quarterly 51, 2005, 247-253. .dvi file, LaTeX file.
- "Diamond, Square, and Level by Level Equivalence", Archive for Mathematical Logic 44, 2005, 387-395. .dvi file, LaTeX file.
- "On a Problem of Foreman and Magidor", Archive for Mathematical Logic 44, 2005, 493-498. .dvi file, LaTeX file.
- (with G. Sargsyan) "Can A Large Cardinal Be Forced From A Condition Implying Its Negation?", Proceedings of the American Mathematical Society 133, 2005, 3103-3108. .dvi file, LaTeX file.
- "Universal Partial Indestructibility and Strong Compactness", Mathematical Logic Quarterly 51, 2005, 524-531. .dvi file, LaTeX file.
- "Universal Indestructibility is Consistent with Two Strongly Compact Cardinals", Bulletin of the Polish Academy of Sciences (Mathematics) 53, 2005, 131-135. .dvi file, LaTeX file.
- (with G. Sargsyan) "Identity Crises and Strong Compactness III: Woodin Cardinals", Archive for Mathematical Logic 45, 2006, 307-322. .dvi file, LaTeX file.
- "Indestructibility and Strong Compactness", Proceedings of Logic Colloquium 2003, Lecture Notes in Logic 24, 2006, 27-37. .dvi file, LaTeX file.
- "How Many Normal Measures Can $\aleph_{\omega + 1}$ Carry?", Fundamenta Mathematicae 191, 2006, 57-66. .dvi file, LaTeX file.
- "Supercompactness and Measurable Limits of Strong Cardinals II: Applications to Level by Level Equivalence", Mathematical Logic Quarterly 52, 2006, 457-463. .dvi file, LaTeX file.
- (with P. Koepke) "The Consistency Strength of $\aleph_\omega$ and $\aleph_{\omega_1}$ being Rowbottom Cardinals without the Axiom of Choice", Archive for Mathematical Logic 45, 2006, 721-737. .dvi file, LaTeX file.
- "Failures of SCH and Level by Level Equivalence", Archive for Mathematical Logic 45, 2006, 831-838. .dvi file, LaTeX file.
- "The Least Strongly Compact can be the Least Strong and Indestructible", Annals of Pure and Applied Logic 144, 2006, 33-42. .dvi file, LaTeX file.
- "Indestructibility and Level by Level Equivalence and Inequivalence", Mathematical Logic Quarterly 53, 2007, 78-85. .dvi file, LaTeX file.
- "Supercompactness and Level by Level Equivalence are Compatible with Indestructibility for Strong Compactness", Archive for Mathematical Logic 46, 2007, 155-163. .dvi file, LaTeX file.
- "Level by Level Equivalence and the Number of Normal Measures over $P_\kappa(\lambda)$", Fundamenta Mathematicae 194, 2007, 253-265. .dvi file, LaTeX file.
- (with G. Sargsyan) "A Reduction in Consistency Strength for Universal Indestructibility", Bulletin of the Polish Academy of Sciences (Mathematics) 55, 2007, 1-6. .dvi file, LaTeX file.
- (with J. Cummings and J. D. Hamkins) "Large Cardinals with Few Measures", Proceedings of the American Mathematical Society 135, 2007, 2291-2300. .dvi file, LaTeX file.
- "Reducing the Consistency Strength of an Indestructibility Theorem", Mathematical Logic Quarterly 54, 2008, 288-293. .dvi file, LaTeX file.
- (with J. Cummings) "An L-like Model Containing Very Large Cardinals", Archive for Mathematical Logic 47, 2008, 65-78. .dvi file, LaTeX file.
- "Indestructibility and Measurable Cardinals with Few and Many Measures", Archive for Mathematical Logic 47, 2008, 101-110. .dvi file, LaTeX file.
- (with G. Sargsyan) "Universal Indestructibility for Degrees of Supercompactness and Strongly Compact Cardinals", Archive for Mathematical Logic 47, 2008, 133-142. .dvi file, LaTeX file.
- (with P. Koepke) "Making All Cardinals Almost Ramsey", Archive for Mathematical Logic 47, 2008, 769-783. .dvi file, LaTeX file.
- "On the Number of Normal Measures $\aleph_1$ and $\aleph_2$ can Carry", Tbilisi Mathematical Journal 1, 2008, 9-14. Note: This paper may be accessed online at http://ncst.org.ge/Journals/TMJ/ by clicking on the link "Most recent volume". .dvi file, .pdf file, LaTeX file.
- "A Note on Indestructibility and Strong Compactness", Bulletin of the Polish Academy of Sciences (Mathematics) 56, 2008, 191-197. .dvi file, .pdf file, LaTeX file.
- "Stationary Reflection and Level by Level Equivalence", Colloquium Mathematicum 115, 2009, 113-128. .dvi file, .pdf file, LaTeX file.
- "Indestructibility and Stationary Reflection", Mathematical Logic Quarterly 55, 2009, 228-236. .dvi file, .pdf file, LaTeX file.
- "Indestructibility under Adding Cohen Subsets and Level by Level Equivalence", Mathematical Logic Quarterly 55, 2009, 271-279. .dvi file, .pdf file, LaTeX file.
- "Indestructibility, Strong Compactness, and Level by Level Equivalence", Fundamenta Mathematicae 204, 2009, 113-126. .dvi file, .pdf file, LaTeX file.
- "Sandwiching the Consistency Strength of Two Global Choiceless Cardinal Patterns", Bulletin of the Polish Academy of Sciences (Mathematics) 57, 2009, 189-197. .dvi file, .pdf file, LaTeX file.
- "L-like Combinatorial Principles and Level by Level Equivalence", Bulletin of the Polish Academy of Sciences (Mathematics) 57, 2009, 199-207. .dvi file, .pdf file, LaTeX file.
- "Tallness and Level by Level Equivalence and Inequivalence", Mathematical Logic Quarterly 56, 2010, 4-12. .dvi file, .pdf file, LaTeX file.
- (with G. Sargsyan) "An Equiconsistency for Universal Indestructibility", Journal of Symbolic Logic 75, 2010, 314-322. .dvi file, .pdf file, LaTeX file.
- "How Many Normal Measures Can $\aleph_{\omega_1 + 1}$ Carry?", Mathematical Logic Quarterly 56, 2010, 164-170. .dvi file, .pdf file, LaTeX file.
- (with P. Koepke) "The Consistency Strength of Choiceless Failures of SCH", Journal of Symbolic Logic 75, 2010, 1066-1080. .dvi file, .pdf file, LaTeX file.
- "Indestructibility, Instances of Strong Compactness, and Level by Level Inequivalence", Archive for Mathematical Logic 49, 2010, 725-741. .dvi file, .pdf file, LaTeX file.
- "Indestructibility, HOD, and the Ground Axiom", Mathematical Logic Quarterly 57, 2011, 261-265. .dvi file, .pdf file, LaTeX file.
- "A Remark on the Tree Property in a Choiceless Context", Archive for Mathematical Logic 50, 2011, 585-590. .dvi file, .pdf file, LaTeX file.
- (with Sh. Friedman) "Coding into HOD via Normal Measures with Some Applications", Mathematical Logic Quarterly 57, 2011, 366-372. .dvi file, .pdf file, LaTeX file, .bib file.
- "Level by Level Inequivalence beyond Measurability", Archive for Mathematical Logic 50, 2011, 707-712. .dvi file, .pdf file, LaTeX file.
- "Indestructibility, Measurability, and Degrees of Supercompactness", Mathematical Logic Quarterly 58, 2012, 75-82. .dvi file, .pdf file, LaTeX file.
- (with V. Gitman and J. D. Hamkins) "Inner Models with Large Cardinal Features Usually Obtained by Forcing", Archive for Mathematical Logic 51, 2012, 257-283. .dvi file, .pdf file, LaTeX file, .bib file.
- "Some Applications of Sargsyan's Equiconsistency Method", Fundamenta Mathematicae 216, 2012, 207-222. .dvi file, .pdf file, LaTeX file.
- "The Wholeness Axioms and the Class of Supercompact Cardinals", Bulletin of the Polish Academy of Sciences (Mathematics) 60, 2012, 101-111. .dvi file, .pdf file, LaTeX file.
- (with M. Gitik and G. Sargsyan) "Indestructible Strong Compactness but not Supercompactness", Annals of Pure and Applied Logic 163, 2012, 1237-1242. .dvi file, .pdf file, LaTeX file.
- "Level by Level Inequivalence, Strong Compactness, and GCH", Bulletin of the Polish Academy of Sciences (Mathematics) 60, 2012, 201-209. .dvi file, .pdf file, LaTeX file.
- "More Easton Theorems for Level by Level Equivalence", Colloquium Mathematicum 128, 2012, 69-86. .dvi file, .pdf file, LaTeX file.
- "On Some Questions Concerning Strong Compactness", Archive for Mathematical Logic 51, 2012, 819-829. .dvi file, .pdf file, LaTeX file.
- (with S. Jackson and B. Loewe) "Cofinality and Measurability of the First Three Uncountable Cardinals", Transactions of the American Mathematical Society 365, 2013, 59-98. .dvi file, .pdf file, LaTeX file, .bib file.
- (with B. Cody) "Consecutive Singular Cardinals and the Continuum Function", Notre Dame Journal of Formal Logic 54, 2013, 125-136. .dvi file, .pdf file, LaTeX file.
- (with J. Cummings and J. D. Hamkins) "Singular Cardinals and Strong Extenders", Central European Journal of Mathematics 11, 2013, 1628-1634. .dvi file, .pdf file, LaTeX file.
- "Indestructible Strong Compactness and Level by Level Inequivalence", Mathematical Logic Quarterly 59, 2013, 371-377. .dvi file, .pdf file, LaTeX file.
- "Some Remarks on Tall Cardinals and Failures of GCH", Bulletin of the Polish Academy of Sciences (Mathematics) 61, 2013, 97-106. .dvi file, .pdf file, LaTeX file.
- "A Note on Powers of Singular Strong Limit Cardinals", Infinity, Computability, and Metamathematics: Festschrift celebrating the 60th birthdays of Peter Koepke and Philip Welch, College Publications, Volume 23, 2014, 1-3. .dvi file, .pdf file, LaTeX file.
- "Singular Failures of GCH and Level by Level Equivalence", Bulletin of the Polish Academy of Sciences (Mathematics) 62, 2014, 11-21. .dvi file, .pdf file, LaTeX file.
- (with M. Gitik) "On Tall Cardinals and Some Related Generalizations", Israel Journal of Mathematics 202, 2014, 343-373. .dvi file, .pdf file, LaTeX file.
- "Inaccessible Cardinals, Failures of GCH, and Level by Level Equivalence", Notre Dame Journal of Formal Logic 55, 2014, 431-444. .dvi file, .pdf file, LaTeX file.
- (with P. Koepke and I. Dimitriou) "The First Measurable Cardinal can be the First Uncountable Regular Cardinal at Any Successor Height", Mathematical Logic Quarterly 60, 2014, 471-486. .pdf file, LaTeX file, .bib file.
- (with Sh. Friedman) "HOD-Supercompactness, Indestructibility, and Level by Level Equivalence", Bulletin of the Polish Academy of Sciences (Mathematics) 62, 2014, 197-209. .dvi file, .pdf file, LaTeX file, .bib file.
- "A Universal Indestructibility Theorem Compatible with Level by Level Equivalence", Archive for Mathematical Logic 54, 2015, 463-470. .pdf file, LaTeX file.
- "Mixed Levels of Indestructibility",
Bulletin of the Polish Academy of Sciences (Mathematics) 63, 2015, 113-122.
.pdf file,
LaTeX file.
- "Indestructible Strong Compactness and Level by Level Equivalence with No Large Cardinal Restrictions", Bulletin of the Polish Academy of Sciences (Mathematics) 63, 2015, 185-194. .pdf file, LaTeX file.
- "Indestructibility and Destructible Measurable Cardinals", Archive for Mathematical Logic 55, 2016, 3-18. .pdf file, LaTeX file.
- "A Note on Tall Cardinals and Level by Level Equivalence", Mathematical Logic Quarterly 62, 2016, 128-132. .pdf file, LaTeX file.
- (with P. Koepke and I. Dimitriou) "All Uncountable Cardinals in the Gitik Model are Almost Ramsey and Carry Rowbottom Filters", Mathematical Logic Quarterly 62, 2016, 225-231. .pdf file, LaTeX file, .bib file.
- "Indestructibility and the Levinski Property", Sarajevo Journal of Mathematics 12, 2016, 3-16. .pdf file, LaTeX file.
- "Precisely Controlling Level by Level Behavior", Mathematical Logic Quarterly 63, 2017, 77-84. .pdf file, LaTeX file.
- "A New Easton Theorem for Supercompactness and Level by Level Equivalence", Bulletin of the Polish Academy of Sciences (Mathematics) 65, 2017, 1-10. .pdf file, LaTeX file.
- "On the Consistency Strength of Level by Level Inequivalence", to appear in the Archive for Mathematical Logic (the special volume in honor of Jim Baumgartner). .pdf file, LaTeX file.
- (with D. Adolf and
P. Koepke)
"Singularizing Successor Cardinals by Forcing",
to appear in Proceedings of the American Mathematical Society.
.pdf file,
LaTeX file.
- "Normal Measures and Strongly Compact Cardinals", to appear in Bollettino dell'Unione Matematica Italiana. .pdf file, LaTeX file.
- (with J. Cummings) "Normal Measures on a Tall Cardinal", submitted for publication to the Journal of Symbolic Logic. .pdf file, LaTeX file.
- "The Enhanced Levinski Property and the Class of Supercompact Cardinals", submitted for publication to the Kobe Journal of Mathematics. .pdf file, LaTeX file.
- "The Consistency of V = HOD with Level by Level Equivalence", submitted for publication to the Journal of the Mathematical Society of Japan. .pdf file, LaTeX file.
- "Tall, Strong, and Strongly Compact Cardinals", submitted for publication to the Archive for Mathematical Logic. .pdf file, LaTeX file.