Imaginaries in bounded pseudo real closed fields

TL;DR

This paper proves that in bounded pseudo real closed fields, the theory eliminates imaginaries when expanded by constants, simplifying the understanding of definable sets and types in such fields.

Contribution

It establishes the elimination of imaginaries in the theory of bounded PRC fields with constants, a significant step in model theory of these fields.

Findings

Th(M) eliminates imaginaries in bounded PRC fields with constants

Simplifies the classification of definable sets in these fields

Advances understanding of model-theoretic properties of PRC fields

Abstract

The main result of this paper is that if M is a bounded PRC field then Th(M) eliminates imaginaries in the language of rings expanded by constant symbols.