Akihiro Kanamori

Department of Mathematics
Boston University
111 Cummington Mall
Boston, Massachusetts 02215, USA

Phone: (617) 353-9538
FAX: (617) 353-8100

Email: aki@math.bu.edu

Office: MCS 248

A shorter curriculum vitae

Books

The Higher Infinite, 536pp, Springer, Berlin, November 1994. Introduction
- Corrected second printing, May 1997
- Japanese translation, November 1998
- Second edition, April 2003
- Corrected second printing of second edition, March 2005
- Softcover edition, December 2008
- New reprinting, Springer--Beijing World Publishing, 2012
- ISBN 978-3-540-88866-6 e-ISBN 978-3-540-88867-3
(editor) Analytic Philosophy and Logic, The Proceedings of the Twentieth World Congress of Philosophy, Volume 6, 303pp, Philosophy Documentation Center, Bowling Green, 2000. Introduction
(set theory editor) International Directory of Logicians: Who's Who in Logic, with managing editors Dov M. Gabbay and John H. Woods, College Publications, 2009.
(editor with Matthew Foreman), Handbook of Set Theory, 2197pp in three volumes, Springer, Berlin, 2010. ISBN 978-1-4020-4843 e-ISBN 978-4020-5764-9 Introduction
(editor with Heinz-Dieter Ebbinghaus) Collected Works of Ernst Zermelo, Volume I, 654pp, Springer, Berlin, 2010.
(editor) Sets and Extensions in the Twentieth Century, 865pp, with managing editors Dov M. Gabbay and John H. Woods, Cambridge University Press, Cambridge, 2012. Preface
(editor with Heinz-Dieter Ebbinghaus) Collected Works of Ernst Zermelo, Volume II, 781pp, Springer, Berlin, 2013.
Essays on Set Theory, 593pp, Studies in Logic, Mathematical Logic and Foundations, vol. 89, College Publications, London, 2021. ISBN 978-1-84890-357-9

Publications before 1995

The siege of Chitral as an imperial factor, Journal of Indian History 46(3)(1968), 387-404.
Weakly normal filters and irregular ultrafilters, Transactions of the American Mathematical Society 220(1976), 393-399.
Ultrafilters over a measurable cardinal, Annals of Mathematical Logic 11(1976), 315-356.
Some combinatorics involving ultrafilters, Fundamenta Mathematicae 100(1978), 145-155.
Strong axioms of infinity and elementary embeddings, with William N. Reinhardt and Robert M. Solovay, Annals of Mathematical Logic 13(1978), 73-116.
The evolution of large cardinal axioms in set theory, with Menachem Magidor, in: Gert H. Müller and Dana S. Scott, editors, Higher Set Theory (Proceedings, Oberwolfach, Germany 1977), Lecture Notes in Mathematics 669, 99-275. Springer-Verlag, Berlin, 1978.
On Vopenka's and related principles, in: Angus MacIntyre, Leszek Pacholski, and Jeffrey Paris, editors, Logic Colloquium '77, 145-153. North-Holland, Amsterdam, 1978.
On p-points over a measurable cardinal, The Journal of Symbolic Logic 46(1981), 59-65.
Perfect-set forcing for uncountable cardinals, Annals of Mathematical Logic 19(1980), 97-114.
Morass-level combinatorial principles, in: George Metakides, editor, Patras Logic Symposion, 339-358. North-Holland, Amsterdam, 1982.
On Silver's and related principles, in: Dirk van Dalen, Daniel Lascar, and Timothy Smiley, editors, Logic Colloquium '80, 153-172. North-Holland, Amsterdam, 1982.
Morasses in combinatorial set theory, in: A.R.D. Mathias, editor, Surveys in Set Theory, 167-196. Cambridge University Press, Cambridge, 1983.
Filters for square-bracket partition relations, with James M. Henle and Eugene M. Kleinberg, Zeitschrift für Mathematische Logik und Grundlagen der Mathematik 30(1984), 183-192.
Separating ultrafilters on uncountable cardinals, with Alan D. Taylor, Israel Journal of Mathematics 47(1984), 131-148.
Negative partition relations for ultrafilters on uncountable cardinals, with Alan D. Taylor, Proceedings of the American Mathematical Society 92(1984), 83-93.
Partition relations for successor cardinals, Advances in Mathematics 59(1986), 152-169.
Finest partitions for ultrafilters, The Journal of Symbolic Logic 51(1986), 327-332.
A proposal for deciding chess matches, with Leonid Levin, Players' Chess News, Games and Events 56, 26 August 1985.
On Gödel incompleteness and finite combinatorics, with Kenneth McAloon, Annals of Pure and Applied Logic 33(1987), 23-41.
Diamonds, large cardinals, and ultrafilters, in Walter A. Carnielli and Luiz Paulo de Alcantara, editors, Methods and Applications of Mathematical Logic, Contempoaray Mathematics 69, 35-42. American Mathematical Society, Providence, 1988.
Regressive partition relations for infinite cardinals, with András Hajnal and Saharon Shelah, Transactions of the American Mathematical Society 299(1987), 145-155.
Regressive partitions and Borel diagonalization, The Journal of Symbolic Logic 54(1989), 540-552.
The compleat 0-dagger, with Tamara Awerbuch-Friedlander, Zeitschrift für Mathematische Logik and Grundlagen der Mathematik 36(1990), 133-141.
Regressive partition relations, n-subtle cardinals, and Borel diagonalization, Annals of Pure and Applied Logic 52(1991), 65-77.

Publications since 1995

Complete quotient Boolean algebras, with Saharon Shelah, Transactions of the American Mathematical Society 347(1995), 1963-1979.
The emergence of descriptive set theory, in Jaakko Hintikka, editor, From Dedekind to Gödel: Essays on the Development of the Foundations of Mathematics, Synthese Library volume 251, 241-262. Dordrecht,Kluwer 1995.
Hilbert and set theory, with Burton Dreben, Synthese 110(1997), 77-125.
The mathematical import of Zermelo's Well-Ordering Theorem, The Bulletin of Symbolic Logic 3(1997), 281-311.
Introduction to Akihiro Kanamori, editor, Analytic Philosophy and Logic, The Proceedings of the Twentieth World Congress of Philosophy, Volume 6, 1998, xziii-xli. Philosophy Documentation Center, Bowling Green, 2000.
Does GCH imply AC locally?, with David Pincus, in Gábor Halász, László Lovász, Miklós Simonivits and Vera T. Sós, editors, Paul Erdös and His Mathematics, Bolyai Society Mathematical Studies, volume II, 413-426. Berlin, Springer, 2002.
The empty set, the singleton, and the ordered pair, The Bulletin of Symbolic Logic 9(2003), 273-298.
Introductory note to the Gödel-Ulam correspondence, in Solomon Feferman and John W. Dawson, Jr., editors-in-chief, Kurt Gödel Collected Works, Volume V, Correspondence H-Z. Clarendon Press, Oxford, 2003.
Zermelo and set theory, The Bulletin of Symbolic Logic 10(2004), 487-553.
Levy and set theory, Annals of Pure and Applied Logic 140(2006), 233-252.
How Gödel transformed set theory, with Juliet Floyd, Notices of the American Mathematical Society 53(2006), 417-425.
Gödel and set theory, The Bulletin of Symbolic Logic 13(2007), 153-188. Reprinted in Solomon Feferman, Charles Parsons, and Stephen G. Simpson, editors, Kurt Gödel: Essays for his Centennial, Lecture Notes in Logic, volume 33, 145-180. Associaton for Symbolic Logic, 2010.
Cohen and set theory, The Bulletin of Symbolic Logic 14(2008), 351-378.
L'ipotesi del continuo (in Italian), a book chapter in: Claudio Bartocci and Piergiorgio Odifreddi, editors, Mathematics and Culture, volume 2, 461-514. Einaudi 2008.
Set theory from Cantor to Cohen, a book chapter in: Andrew D. Irvine, editor, Philosophy of Mathematics, volume 4 of Handbook of the Philosophy of Science, 395-460. Cambridge University Press, Cambridge, 2009. Revised version of BSL 2(1996), 1-71 article above. Reprinted with minor emendations in Dov M. Gabbay, Akihiro Kanamori, and John H. Woods, editors, Sets and Extensions in the Twentieth Century, volume 6 of Handbook for the History of Logic, 1-71. Cambridge University Press, Cambridge, 2012.
Bernays and set theory, The Bulletin of Symbolic Logic 15(2009), 43-60.
The infinite as method in set theory and mathematics, Ontology Studies 9(2009), 31-41.
Introduction to Matthew Foreman and Akihiro Kanamori, editors, Handbook of Set Theory, 1-92. Springer, Berlin, 2010.
Introductory note to 1930a, Zermelo's article ``Über Grenzzahlen und Mengenbereiche'', in: Heinz-Dieter Ebbinghaus and Akihiro Kanamori, editors, Collected Works of Ernst Zermelo, Volume I, 390-431. Springer, Berlin, 2010.
Introductory note to s1930d, Zermelo's report to the Notgemeinschaft der Deutschen Wissenschaft, in: Heinz-Dieter Ebbinghaus and Akihiro Kanamori, editors, Collected Works of Ernst Zermelo, Volume I, 432-443. Springer, Berlin, 2010.
Introductory note to s1930e, Zermelo's note on the cumulative hierarchy conception of sets, in: Heinz-Dieter Ebbinghaus and Akihiro Kanamori, editors, Collected Works of Ernst Zermelo, Volume I, 444-453. Springer, Berlin, 2010.
Introductory note to s1931e and s1933b, Zermelo's notes on ordinal numbers and large cardinals, in: Heinz-Dieter Ebbinghaus and Akihiro Kanamori, editors, Collected Works of Ernst Zermelo, Volume I, 502-515. Springer, Berlin, 2010.
Historical remarks on Suslin's Problem, in: Juliette Kennedy and Roman Kossak, editors, Set Theory, Arithmetic and Foundations of Mathematics: Theorems, Philosophies, Lecture Notes in Logic, volume 36, 1-12. Association for Symbolic Logic, 2011.
Kunen and set theory, Topology and its Applications 158(2011), 2446-2459.
In praise of Replacement, The Bulletin of Symbolic Logic 18(2012), 45-90.
Large cardinals with forcing, a book chapter in: Dov M. Gabbay, Akihiro Kanamori, and John H. Woods, editors, Sets and Extensions in the Twentieth Century, volume 6 of Handbook for the History of Logic, 359-413. Cambridge University Press, Cambridge, 2012.
The mathematical infinite as a matter of method, Annals of the Japan Association for Philosophy of Science 20(2012), 3-15.
Mathematical knowledge: Motley and complexity of proof, Annals of the Japan Association for Philosophy of Science 21(2013), 21-35.
Erdös and set theory, The Bulletin of Symbolic Logic 20(2014), 449-496.
Gödel vis-à-vis Russell: From logic and set theory to philosophy, with Juliet Floyd, in: Gabriella Crocco and Eva-Maria Engelen, editors, Kurt Gödel: Philosopher-Scientist, 243-326. Publications de l'Université de Provence, Aix-en-Provence, 2016.
Laver and set theory, Archive for Mathematical Logic, 55(2016), 133-164.
Mathias and set theory, Mathematical Logic Quarterly, 20(2016), 278-294.
Aspect-perception and the history of mathematics, in: Dominic Shaw, Brendan Harrington and Michael Beaney, editors, Aspect Perception after Wittgenstein: Seeing-as and Novelty, 109-130. Routledge, Abingdon, 2018.
Putnam's constructivization argument, in: Geoffrey Hellman and Roy Cook, editors, Hilary Putnam on Logic and Mathematics, Springer, Berlin, 2018, 236-247.
Cantor and continuity, in: Stewart Shapiro and Geoffrey Hellman, editors, The History of Continua, Oxford University Press, Oxford, 2020, 219-254.
Kreisel and Wittgenstein, in: Paul Weingartner and Hans-Peter Leeb, editors, Kreisel's Interests, On the Foundations of Logic and Mathematics, College Publications, London, 2020, 1-32.
Kunen the expositor, to appear in Annals of Pure and Applied Logic, 2022.
The set theory in Godel's Resultate Grundlagen, to appear, 2022.

Course Syllabi

Last Updated: 7/1/21