## Logic Seminar

Silvain Rideau

Berkeley

Imaginaries in pseudo-p-adically closed fields

**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.)

Tuesday December 5, 2017 at 4:00 PM in SEO 427