Unexpected imaginaries in valued fields with analytic structure

TL;DR

This paper presents an example of an imaginary element in valued fields with analytic structure that cannot be represented within the standard geometric sorts used in algebraic settings.

Contribution

It introduces a specific imaginary in valued fields with analytic structure that defies coding in the usual geometric sorts, highlighting differences from algebraic cases.

Findings

Existence of imaginaries not codable in geometric sorts

Differences between valued fields with analytic and algebraic structures

Implications for model theory of valued fields

Abstract

We give an example of an imaginary defined in certain valued fields with analytic structure which cannot be coded in the `geometric' sorts which suffice to code all imaginaries in the corresponding algebraic setting.