Set theory and set theoretical model theory

  1. Two axioms of set theory with applications to logic. Ann. Acad. Sci. Fenn. Ser. A I. Math. Diss. 20:1-19, 1978.

  2. Abstract logic and set theory, I: Definability. In M. Boffa, D. van Dalen and K. McAloon, editors, Logic Colloquium '78, pages 391-421, North-Holland, 1979.

  3. On the Hanf numbers of unbounded logics. In F. Jensen, B. Mayoh and K. Møller, editors, Proceedings from 5th Scandinavian Logic Symposium, pages 309-328, Aalborg University Press, 1979.

  4. Boolean valued models and generalized quantifiers, Annals of Mathematical Logic, 79, pages 1-225, 1980.

  5. The Hanf number of L_{omega_1omega_1} Proceedings of American Mathematical Society 79:294-297, 1980. Abstract in Journal of Symbolic Logic 46(2):442-443, 1981.

  6. Abstract logic and set theory, II: Large cardinals, Journal of Symbolic Logic 47, pages 335-345, 1982.

  7. Generalized quantifiers in models of set theory. In G. Metakides, editor, Patras Logic Symposion, pages 359-371, North-Holland, 1982.

  8. Delta-extension and Hanf numbers. Fundamenta Mathematicae, 115:43-55, 1983.

  9. Set theoretic definability of logics. In J. Barwise and S. Feferman, editors, Model Theoretic Logics, pages 599-643, Springer, 1985.

  10. A Cantor-Bendixson theorem for the space omega_1^omega_1. Fundamenta Mathematicae, 37:187-199, 1991.

  11. Trees and Pi^1_1-subsets of omega_1^omega_1, with Alan Mekler, Journal of Symbolic Logic 58, 1052-1070, 1993. [Errata: The status of the claims about MA on pages 1055-1057 - e.g. Proposition 6 - is uncertain. There is a type-setting mixup at the bottom of page 1055.]

  12. On the number of automorphisms of uncountable models, with Saharon Shelah and Heikki Tuuri, Journal of Symbolic Logic 58, 1402-1418, 1993.

  13. The Ehrenfeucht-Fraïssé game of length omega_1, with Alan Mekler and Saharon Shelah, Transactions of the American Mathematical Society 339, 567-580, 1993.

  14. Reflection of long game formulas, with Heikki Heikkilä, Mathematical Logic Quarterly 40:381-392, 1994.

  15. Games and trees in infinitary logic: A Survey. In M. Krynicki, M. Mostowski and L. Szczerba, editors, Quantifiers, Kluwer Academic Publishers, 105-138, 1995. [The online version here contains remarks about errata in the published version.]

  16. Trees and Ehrenfeucht-Fraïssé games, with Stevo Todorčević. Annals of Pure and Applied Logic, 100, 69-97, 1999.

  17. Stationary sets and infinitary logic, with Saharon Shelah, Journal of Symbolic Logic, 65:1311-1320, 2000.

  18. Games played on partial isomorphisms, with Boban Veličković, Archive for Mathematical Logic 43:1, 19-30, 2004.

  19. J. Stavi and J. Väänänen, Reflection principles for the continuum. Logic and Algebra, ed. Yi Zhang, pp. 59-84, Contemporary Mathematics, Vol 302, AMS, 2002

  20. T. Hyttinen, S. Shelah and J. Väänänen, More on the Ehrenfeucht-Fraïssé game of length omega_1, Fundamenta Mathematicae, 175 (2002), no. 1, 79-96.

  21. M. Džamonja and J. Väänänen, A family of trees with no uncountable branches, Topology Proceedings vol. 28:1, 2004, 113-132.

  22. On Ordinals accessible by infinitary languages, with Saharon Shelah and Pauli Väisänen, Fundamenta Mathematicae 186 (2005), 193-214.

  23. On infinite Ehrenfeucht-Fraïssé games. In: Stefan Bold, Benedikt Löwe, Thoralf Rausch, Johan van Benthem (eds.), Foundations of the Formal Sciences V, Infinite Games, College Publications, London 2007, 279-317.

  24. Recursive Logic Frames, with Saharon Shelah, Math. Logic Quart. 52, No. 2 (2006)

  25. J. Kennedy and J. Väänänen, Applications of regular filters and square principles in model theory, In: Set Theory: Recent Trends and Applications (A. Andretta ed.), Quaderni di Matematica, vol 17, 2005, 111-136.

  26. J. Kennedy, S. Shelah, and J. Väänänen, Regular Ultrafilters and Finite Square Principles, Journal of Symbolic Logic 73(3), 2008, 817-823.

  27. Menachem Magidor and Jouko Väänänen. On Löwenheim-Skolem-Tarski numbers for extensions of first order logic, Journal of Mathematical Logic, 11(1), 87-113, 2011.

  28. A taste of set theory for philosophers. Journal of the Indian Council of Philosophical Research, Vol. XXVII, No. 2. A Special Issue on "Logic and Philosophy Today", 143-163, 2010. Reprinted in "Logic and Philosophy Today" (edited by A. Gupta and J. v. Benthem), College Publications vol 29, 141-162, 2011.

  29. Second order logic or set theory? Bulletin of Symbolic Logic, 18(1), 91-121, 2012.

  30. On second order characterizability, with Tapani Hyttinen and Kaisa Kangas. Logic Journal of the IGPL (2013) 21 (5): 767-787.

  31. Chain models, trees of singular cardinality and dynamic EF-games, with M. Džamonja, Journal of Mathematical Logic, 11(1), 2011, 61 - 85.

  32. Kennedy, S. Shelah, and J. Väänänen, Regular Ultrapowers at Regular Cardinals, Notre Dame Journal of Formal Logic, 56:3, 2015, 417 - 428. ArXiv: arXiv:1307.6396 [math.LO].

  33. Multiverse set theory and absolutely undecidable propositions. in: J. Kennedy (Ed.): Interpreting Gödel, Cambridge University Press, 2014, 180-208.

  34. Internal Categoricity in Arithmetic and Set Theory, with Tong Wang. Notre Dame Journal of Formal Logic, 56:1(2015), 121-134.

  35. Boolean valued second order logic, with Daisuke Ikegami, Notre Dame Journal of Formal Logic, 56:1 (2015), 167-190.

  36. Positional strategies in long Ehrenfeucht-Fraïssé games., with Saharon Shelah and Boban Veličković, Journal of Symbolic Logic 80(1), 2015, 285-300.

  37. On the symbiosis between model-theoretic and set-theoretic properties of large cardinals, with Joan Bagaria. Journal of Symbolic Logic 81(2), 584-604 (2016).

  38. Inner Models from Extended Logics, with J. Kennedy and M. Magidor. Isaac Newton Institute preprint series, January 2016. Submitted to a journal 2018.

  39. A dichotomy theorem for the generalized Baire space and elementary embeddability at uncountable cardinals, with Dorottya Sziraki, Fundamenta Mathematicae, 238(2017), 53-78.

  40. Tracing internal categoricity. Submitted.

  41. An extension of a theorem of Zermelo. Submitted. Version in arXiv.

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