1;95;0c Publications of Jouko Väänänen

Second order logic

  1. Remarks on generalized quantifiers and second-order logics. In Set theory and hierarchy theory, Prace Naukowe Instytutu Matematyki Politechniki Wroclawskiej, Wroclaw, vol. 14 (1977), pages 117-123.

  2. Second order logic and foundations of mathematics, Bulletin of Symbolic Logic, Volume 7, Issue 4, December, 2001.

  3. Second order logic, set theory and foundations of mathematics. Epistemology versus Ontology, Essays of the Philosophy and Foundations of Mathematics in Honor of Per Martin-Löf, Editors: P. Dybjer, S. Lindström, E. Palmgren and G. Sundholm, Log. Epistemol. Unity Sci., 27, Springer, 2012, 371-380.

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

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

  6. Sort logic and foundations of mathematics, in: Infinity and Truth, Edited by: Chitat Chong, Qi Feng, Theodore A Slaman, W Hugh Woodin, Lecture Notes Series of the Institute for Mathematical Sciences, World Scientific, vol. 25, 2014, 171-186. Available in arXiv.org.

  7. An Ehrenfeucht-Fraïssé Game for Lomega1omega, with Tong Wang. Mathematical Logic Quarterly 59, No 4-5, 357-370 (2013).

  8. Breaking the atom with Samson. In: Computation, Logic, Games, and Quantum Foundations. The Many Facets of Samson Abramsky. Essays Dedicated to Samson Abramsky on the Occasion of His 60th Birthday. Editors: Bob Coecke, Luke Ong, Prakash Panangaden, Lecture Notes in Computer Science, volume 7860, 2013, pp. 327-335.

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

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

  11. Categoricity and consistency in second order logic. Inquiry (An Interdisciplinary Journal of Philosophy), 58(1), 2015, 20-27.

  12. Second order logic and set theory. Philosophy Compass, 10 (2015), 463-478.

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

  14. Second-order and Higher-order Logic, Entry in Stanford Encyclopedia of Philosophy, 2019.

  15. Logic and Games, with Wilfrid Hodges, Entry in Stanford Encyclopedia of Philosophy, 2019.

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

  17. Philosophical Uses of Categoricity Arguments, with Penelope Maddy, Elements in the Philosophy of Mathematics. Cambridge: Cambridge University Press. 55 p. (2023).

  18. Model theory of second order logic. In Beyond First Order Model Theory, Volume 2, CRC Press, edited by Jose Iovino, 2023, Chapter 7, 289-304.

  19. On the categoricity of complete second order theories, with Tapio Saarinen and Hugh Woodin. Journal of Symbolic Logic, online first 27 August 2025. Available in arXiv.

  20. Second order logic and Set Theory Redux, to appear in the Oxford Handbook of Philosophy of Set Theory, edited by Luca Incurvati and Giorgio Venturi, Oxford University Press.

Back to the homepage of Jouko Väänänen.