Beautiful pairs in unstable theories and spaces of definable types
Basic data for this talk
Type of talk: scientific talk
Name der Vortragenden: Hils, Martin
Date of talk: 08/03/2023
Talk language: English
Information about the event
Name of the event: Research Seminar in Model Theory
Event period: 08/03/2023
Event location: Universität Wien
Organised by: Kurt Gödel Research Center, Universität Wien
Abstract
By classical results of Poizat, the theory of beautiful pairs of models of a stable theory T is "meaningful" precisely when the set of all definable types in T is strict pro-definable, which is the case if and only if T is nfcp. We transfer the notion of beautiful pairs to unstable theories and study them in particular in henselian valued fields, establishing Ax-Kochen-Ershov principles for various questions in this context. Using this, we show that the theory of beautiful pairs of models of ACVF is "meaningful" and infer the strict pro-definability of various spaces of definable types in ACVF, e.g., the model theoretic analogue of the Huber analytification of an algebraic variety. This is joint work with Pablo Cubides Kovacsics and Jinhe Ye.Keywords: beautiful pairs; valued fields; definable types
Speakers from the University of Münster
| Hils, Martin | Professorship for Mathematical Logic (Prof. Hils) |