A short note on model theory of C((t))

TL;DR

This paper investigates the model-theoretic properties of the field C((t)) within valued rings, characterizing definable compactness and discussing definable groups over this structure.

Contribution

It provides a characterization of definable compactness in C((t)) and offers insights into definable groups in this setting.

Findings

Definable subsets of C((t))^n are compact iff they are closed and unbounded.

Provides comments on the structure of definable groups over C((t)).

Abstract

In this short note, we study C((t)) in the language of valued rings. We show that a definable subset of C((t))n (or in monster model, Mn) is definably compact iff it is closed and unbounded. Then we give some comments on definable groups over C((t)).