Silvain Rideau : Imaginaries in pseudo-p-adically closed fields

Posted by James Freitag , part of the Logic Seminar.

At

Dec. 5, 2017, 4 p.m.

In

SEO 427

Abstract

A field is said to be pseudo-p-adically closed (ppc) if it is existentially closed in every regular extension to which each of its p-adic valuation extends. Recent work of Montenegro led to a much better understanding of the model theory of bounded ppc fields (for example, we now know that they are NTP2). But one natural question was left open: elimination of imaginaries. The goal of this talk will be to show how the lack of interaction between the p-adic valuations of a bounded ppc field can be used to classify its imaginaries and show that they can all be described in terms of the imaginaries induced by each valuation. I will also describe a general criterion for elimination of imaginaries, inspired by the proofs of that result in various simple theories, combining quantifier free invariant extensions of types and amalgamation. Joint with Samaria Montenegro.)