Imaginaries in separably closed valued fields

TL;DR

This paper proves that certain algebraic structures called separably closed valued fields eliminate imaginaries in a geometric language, and studies their model-theoretic properties like metastability and types.

Contribution

It establishes elimination of imaginaries for these fields and analyzes the structure of stably dominated types within them.

Findings

Separable closed valued fields of finite imperfection degree are metastable.

The space of stably dominated types is strict pro-definable.

Classification of interpretable sets aids in understanding model-theoretic properties.

Abstract

We show that separably closed valued fields of finite imperfection degree (either with lambda-functions or commuting Hasse derivations) eliminate imaginaries in the geometric language. We then use this classification of interpretable sets to study stably dominated types in those structures. We show that separably closed valued fields of finite imperfection degree are metastable and that the space of stably dominated types is strict pro-definable.