1;95;0c Publications of Jouko Väänänen

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 claim that MA implies there is a maximal tree in TO is false, as shown by Dzamonja and Shelah, see here. There is also an unfortunate 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). ArXiv.

  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. ArXiv.

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

  39. An extension of a theorem of Zermelo. Bulletin of Symbolic Logic, 25(2), 208-212, 2019. Available in ArXiv.

  40. Tracing internal categoricity. Theoria vol. 87 (4), 986-1000 (2021). Available in ArXiv.

  41. Inner Models from Extended Logics: Part 1, with J. Kennedy and M. Magidor. Journal of Mathematical Logic Vol. 21, No. 2 (2021), Online Ready.

  42. Inner Models from Extended Logics: Part 2, with J. Kennedy and M. Magidor. Submitted. Available in arXiv.

  43. Bounded Symbiosis and Upwards Reflection, with Lorenzo Galeotti and Yurii Khomskii, to appear. Available in arXiv.

  44. Logicality and model classes, with Juliette Kennedy. Bulletin of Symbolic Logic (to appear). Available in arXiv.

  45. A syntactic approach to Shelah’s logic L^1_\kappa, with Andres Villaveces, to appear.

  46. When cardinals determine the power set: inner models and Härtig quantifier logic, with P. Welch, to appear.

  47. On the categoricity of complete second order theories, with Hugh Woodin. To appear.

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