Open cell property in weakly o-minimal structures

TL;DR

This paper proves that in weakly o-minimal structures, every bounded definable open set can be expressed as a finite union of open strong cells, extending understanding of cell decomposition in such structures.

Contribution

It establishes that bounded definable open sets are finite unions of open strong cells in weakly o-minimal structures, providing a new decomposition result.

Findings

Bounded definable open sets are finite unions of open strong cells.

Proved a theorem similar to the main result.

Enhanced understanding of cell decomposition in weakly o-minimal structures.

Abstract

Every bounded definable open set is a union of finitely many open strong cells in a weakly o-minimal expansion of a real closed field. We prove this fact and another theorem similar to it.