Logic Seminar - Martin Hils

Wed, 26/05/202111:00-13:00
beautiful pairs of valued fields and spaces of definable types

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.