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: 26/05/2021
Talk language: English
Information about the event
Name of the event: Logic Seminar
Event period: 26/05/2021
Event location: The Hebrew University of Jerusalem, Jerusalem, Israel
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.Speakers from the University of Münster
| Hils, Martin | Professorship for Mathematical Logic (Prof. Hils) |