Beautiful pairs of valued fields and spaces of definable types
Basic data for this talk
Type of talk: scientific Talk
Name der Vortragenden: Hils, Martin
Date of talk: 08/04/2021
Talk language: English
Information about the event
Name of the event: Seminario di logica
Event period: 08/04/2021
Event location: Università degli studi della Campania Luigi Vanvitelli, Caserta, Italien
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 nfpc. We transfer the notion of beautiful pairs to unstable theories and study them in particular in 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 stable completion introduced by Hrushovski-Loeser, and a model theoretic analogue of the Huber analytification of an algebraic variety.This is work in progress, joint with Pablo Cubides Kovacsics and Jinhe Ye.Keywords: model theory; definable types; valued fields
Speakers from the University of Münster
| Hils, Martin |
Projects the talk is about
Duration: 01/01/2020 - 31/12/2024 Funded by: DFG - Individual Grants Programme Type of project: Individual project | |
Duration: 01/01/2019 - 31/12/2025 | 1st Funding period Funded by: DFG - Cluster of Excellence Type of project: Main DFG-project hosted at University of Münster |
Publications referred to in the talk
Cubides Kovacsics Pablo, Hils Martin, Ye Jinhe (2021) In: ((Bitte Journal prüfen)), 2021. Research article (journal) | submitted / under review |