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Models and Games

Lecturer: Jouko Väänänen

(University of Helsinki, Finland and University of Amsterdam, The Netherlands)

This is an introduction to model theory based on a careful analysis of some important games occurring in logic. We cover the following topics: Two-person games of perfect information, the Ehrenfeucht-Fraisse Game and elementary equivalence, the Cub Game and the Lowenheim-Skolem Theorem, the Semantic Game and the truth definition, the Model Existence Game and the Compactness Theorem. Time permitting, we cover also topics in dependence logic, infinitary logic and generalized quantifiers. Some of the methods apply to finite models as well as infinite ones. Some are relevant only in infinite models.

The course is based on the book: J. Vaananen: Models and Games (Cambridge University Press, 2011)

Download: book_partial_Chongqing.pdf dependence_logic_short_version.pdf (for Lec 5)

Course slides: Lec 1 Lec 2 Lec 3 Lec 4 Lec 5

Handouts: Lec 1 Lec 2 Lec 3 Lec 4 Lec 5