An analogue of the Baire Category Theorem

TL;DR

This paper demonstrates that in any definably complete expansion of an ordered field, an analogue of the classical Baire Category Theorem holds, extending its applicability within model theory and real algebraic geometry.

Contribution

It establishes a new version of the Baire Category Theorem applicable to definably complete expansions of ordered fields, broadening the theorem's scope.

Findings

Every definably complete expansion satisfies the analogue

The analogue parallels the classical Baire Category Theorem

Implications for model theory and real algebraic geometry

Abstract

Every definably complete expansion of an ordered field satisfies an analogue of the Baire Category Theorem.