Spaces of definable types and beautiful pairs in unstable theories

Basic data for this talk

Type of talk: scientific Talk

Name der Vortragenden: Hils, Martin

Date of talk: 21/04/2023

Talk language: English

Information about the event

Name of the event: Géométrie et théorie des modèles

Event period: 21/04/2023

Event location: Institut Henri Poincaré, Paris

Event website: http://gtm.imj-prg.fr/archives2223.html

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: model theory; beautiful pairs; valued fields; definable types

Speakers from the University of Münster

Hils, Martin

Professorship for Mathematical Logic (Prof. Hils)

Projects the talk is about

Geometric and Combinatorial Configurations in Model Theory (GeoMod) Duration: 01/01/2020 - 31/12/2024 Funded by: DFG - Individual Grants Programme Type of project: Individual project
EXC 2044 - A2: Groups, model theory and sets Duration: 01/01/2019 - 31/12/2025 \| 1st Funding period Funded by: DFG - Cluster of Excellence Type of project: Subproject in DFG-joint project hosted at University of Münster

Publications referred to in the talk

Beautiful pairs

Cubides Kovacsics Pablo, Hils Martin, Ye Jinhe (2021)

In: ((Bitte Journal prüfen)), 2021.

Research article (journal) | submitted / under review