Finite model theory

  1. Generalized quantifiers and pebble games on finite structures, with Phokion Kolaitis, Annales of Pure and Applied Logic 74(1995), 23-75, Short version appeared in: Proceedings of the 7th IEEE Symposium on Logic in Computer Science, 1992.

  2. The Hierarchy Theorem for generalized quantifiers, with Lauri Hella and Kerkko Luosto, Journal of Symbolic Logic 61(3):802-817, 1996.

  3. Combinatorics and Quantifiers, with Jaroslav Nesetril, Commentat. Math. Univ. Carol. 37(3), 1996.

  4. Definability of polyadic lifts of generalized quantifiers, with Lauri Hella and Dag Westerståhl, Journal of Logic, Language and Information. 6:305-335, 1997.

  5. Unary quantifiers on finite models, Journal of Logic, Language and Information. 6:275-304, 1997.

  6. Generalized quantifiers. Bulletin of the European Association for Theoretical Computer Science. June 1997.

  7. Quantifiers and congruence closure, with Jörg Flum and Mattias Schielen, Studia Logica 62:3, 315-340, 1999.

  8. with D. Westerståhl, On the expressive power of monotone natural language quantifiers over finite sets, Journal of Philosophical Logic, 31(2002), 327--358.

  9. J. Väänänen, Pseudo-finite model theory, Matematica Contemporanea vol 24, 2003, 169-183.

  10. R. Parikh and J. Väänänen, Finite information logic, Annals of Pure and Applied Logic vol. 134, 2005, 83-93

  11. Balder ten Cate, Johan van Benthem and Jouko Väänänen. Lindström theorems for fragments of first-order logic. Proceedings of LICS 2007, pp 280-292. Journal version: Logical Methods in Computer Science 5(3) (2009) 1 - 27.

  12. The Size of a Formula as a Measure of Complexity, with Lauri Hella, in Logic Without Borders: Essays on Set Theory, Model Theory, Philosophical Logic and Philosophy of Mathematics, edited by Åsa Hirvonen, Juha Kontinen, Roman Kossak and Andrés Villaveces, De Gruyter, 2015, 193-214. Available in arXiv.org.