PUBLICATIONS 1. “On Embedding Models of Arithmetic into

1. “On Embedding Models of Arithmetic into Reduced Powers,” Ph.D. thesis, City University of New York, 1996.
2. (with Saharon Shelah) “On Regular Reduced Products”, Journal of Symbolic Logic, volume 67, 2002, 1169-1177.
3. “History of Logic (vol. 1)”, editor (with Gabriel Sandu), Synthese, volume
137 (1), 2003.
4. “History of Logic (vol. 2)”, editor, Synthese, volume 137 (2), 2003.
5. (with Saharon Shelah) “On Embedding Models of Arithmetic of Cardinality ℵ1 into Reduced Powers”, Fundamenta Mathematicae, volume 176
(1), 2003.
6. “On Embedding Models of Arithmetic into Reduced Powers”, Matematica
Contemporanea, volume 24, 2003, 91-115.
7. (with Mark van Atten) “The Philosophical Development of Kurt Gödel”,
Bulletin of Symbolic Logic, volume 9 (4), 2003, 425–476. Reprinted in
Kurt Gödel, Essays for his Centennial, Feferman, Parsons, Simpson (eds.),
Lecture Notes in Logic (33), 2010.
8. (with Mark van Atten) “Gödel’s Modernism: On Set-Theoretic Incompleteness”, Graduate Faculty Philosophy Journal, 25 (2), 2004, 289–349.
9. (with Saharon Shelah) “More on Regular Reduced Products”, Journal of
Symbolic Logic, volume 69 (4), 2004, 1261–1266.
10. (with Jouko Väänänen) “On Applications of Transfer Principles in Model
Theory”, in Set Theory: Recent Trends and Applications, (A. Andretta
ed.), Quaderni di Matematica, volume 17, 2007, 111–136.
11. “Kurt Gödel”, The Stanford Encyclopedia of Philosophy, (Edward N. Zalta,
ed.), (electronic publication,, 2007.
12. “Aesthetics and Mathematics”, The Reasoner, volume 2 (2), February
13. (with Saharon Shelah and Jouko Väänänen) “Regular Ultrafilters and Finite Square Principles”, Journal of Symbolic Logic, volume 73 (2), September 2008, 817–823.
14. (with Mark van Atten) “Gödel’s Modernism Revisited”, in Logicism, Intuitionism and Formalism: What has become of them?, (Lindstrm, S.;
Palmgren, E.; Segerberg, K.; Stoltenberg-Hansen, V. (Eds.), Synthese Library, volume 341, Springer, 2009.
15. (with Mark van Atten) “Gödel’s Logic”, in The Handbook of History of
Logic: Logic from Russell to Gödel, (Gabbay and Woods, eds.), Elsevier,
Amsterdam, volume 5, 2009.
16. “Gödel’s Thesis: An Appreciation”, for the proceedings of the Gödel Centenary meeting “Horizons of Truth,” (Matthias Baaz et al, eds.), Cambridge University Press, 2011.
17. Edited volume (with Roman Kossak): Set Theory, Arithmetic and Foundations of Mathematics: Theorems and Philosophies, Lecture Notes in
Logic (36), Cambridge University Press, 2011.
18. Editorial introduction, edited volume (with Jaap van Oosten): Set theory,
Classical and Constructive, special issue of APAL, to appear.
19. Edited volume: Interpreting Gödel, Cambridge University Press, to appear.
20. “Gödel and Formalization,” contribution to edited volume Interpreting
Gödel, Cambridge University Press, to appear.
21. Editorial introduction, edited volume: Interpreting Gödel, Cambridge University Press, to appear.
22. “On Formalism Freeness: Implementing Gödels 1946 Princeton Bicentennial Lecture,” Bulletin of Symbolic Logic, volume 19, issue 3, September
2013, 351-393.
23. “Regular Ultraproducts at Regular Cardinals,” with S. Shelah, and J.
Väänänen, Notre Dame Journal of Formal Logic, accepted, to appear.
24. “Grounding Effectivity,” proceedings of the conference Turing 100 at Boston
University, November 2012, to appear.
25. On the “Logic without Borders” Point of View, for the proceedings volume
Logic without Borders, to appear.
1. Review of Incompleteness: The Proof and Paradox of Kurt Gödel by R.
Goldstein, Notices of the American Mathematics Society, special issue on
Kurt Gödel, April 2006, 448–455.
2. Review of Kurt Gödel: Das Album by K. Sigmund, J. Dawson and K.
Mühlberger, The Mathematical Intelligencer, vol. 29, issue 3, 2007, 73–
3. Review of The Princeton Companion to Mathematics, (T. Gowers, ed.) in
Bulletin of Symbolic Logic, vol 15(4), December 2009, 431–436.
4. Review of Mathematical Autonomy by C. Franks, Bulletin of Symbolic
Logic, vol. 17(1), 119-122, March, 2011.
1. “On an Incompleteness Theorem in S21 ,” March 1999, abstract of an invited talk given at the San Diego ASL spring meeting, Bulletin of Symbolic
Logic, vol 5, 1999, page 406.
2. (with Saharon Shelah) “On Universality Properties of Reduced Products,”
abstract of a contributed talk in the Logic Colloquium 2000, Paris, Bulletin
of Symbolic Logic, vol. 7, 2001, page 123.
1. “The Continuum Hypothesis,” Institute Letter, Institute for Advanced
Study, Princeton, Fall 2011.
2. “Hilbert’s Twenty-fourth Problem: On the Aesthetic of Simplicity in
Mathematics,” Arkadia Gazette, Helsinki, January 2012.
• Monograph: “The Method of Formal Systems, the Method of Informal
Rigour: Gödel and the Quest for Decidability.” Under contract with
Cambridge University Press.
• (with Menachem Magidor and Jouko Väänänen) “Strong Logics and Constructibility,” in preparation.
1. “Logic Unfettered: European and American Abstraction Now”, Catalogue, Mondrian House Publications, 2007.
2. Book Review: Matti Kujasalo, Galerie Anhava Publications, 2010. Taide
and Design, 10, 2010.
3. Fred Sandback, Taide and Design, 11, 2011.
4. Interview with Andy Goldsworthy, Taide and Design, 13, 2011.
5. Andy Goldsworthy, Pori Art Museum Publications, 2011.
6. “Geometry and Paradoxes of Place: Reflections on the Art of Gabriel
Orozco,” manuscript.