Elementary Equivalence and Ehrenfeucht–Fraissé Games

16.12.2022 14:00 - 14:20

Andrea Vaccaro (Université Paris Cité)




Abstract: Elementary equivalence is a fundamental notion of similarity when it comes to comparison of structures in model theory. Unlike the definitions of isomorphism or elementary submodels, elementary equivalence has a somewhat abstract nature, as it is not witnessed by any concrete map between the structures considered. Ehrenfeucht–Fraissé games and back-and-forth arguments partially fill this gap, by relating elementary equivalence to the existence of families of partial isomorphisms between structures. In this brief lecture I will introduce Ehrenfeucht–Fraissé games, and show how they characterize elementary equivalence for finite relational languages. The intended context for this lecture is a first course in model theory for bachelor and master students.




Dekan R.I. Bot
SR 06, 1. OG, OMP