Logic Seminar

We survey some results in the model theory of metric structures related to different generalisations of the classic Ehrenfeucht–Fraïssé game. Namely, we look at a game of length $\omega$ that is used to characterise separable structures up to different notions of approximate isomorphism (such as linear isomorphisms between Banach spaces) in a framework that resembles that of positive bounded formulas. Additionally, we look at the (finite-length) EF game for continuous first-order logic and its variant of Ehrenfeucht's theorem. Last, we mention recent work on game comonads for continuous logic.

We revisit the model theory of fields with a group action by automorphisms, focusing on the existence of the model companion G-TCF. We explain a flaw in earlier work and present the corrected result: for finitely generated virtually-free groups G, G-TCF exists if and only if G is finite or free. This is joint work with Piotr Kowalski.