# Real closed valued fields with analytic structure

## TL;DR

This paper proves quantifier elimination and weak o-minimality for real closed valued fields with analytic structures, and establishes C-minimality for algebraically closed valued fields with similar structures, advancing model theory in valued fields.

## Contribution

It introduces quantifier elimination results for real closed valued fields with analytic structures and demonstrates weak o-minimality and C-minimality in these contexts, extending previous model-theoretic frameworks.

## Key findings

- Quantifier elimination for real closed valued fields with separated and overconvergent analytic structures.
- Weak o-minimality of these structures.
- C-minimality of algebraically closed valued fields with separated analytic structure.

## Abstract

We show quantifier elimination theorems for real closed valued fields with separated analytic structure and overconvergent analytic structure in their natural one-sorted languages and deduce that such structures are weakly o-minimal. We also provide a short proof that algebraically closed valued fields with separated analytic structure (in any rank) are $C$-minimal.