Dimension functions in weakly o-minimal structures admitting strong cell decomposition

TL;DR

This paper studies the properties and cardinality of dimension functions in weakly o-minimal structures that have strong cell decomposition, contributing to the understanding of their geometric and combinatorial complexity.

Contribution

It introduces the concept of cardinality of dimension functions in such structures and analyzes their behavior, providing new insights into their structural properties.

Findings

Determined bounds for the cardinality of dimension functions.

Established relationships between strong cell decomposition and dimension function complexity.

Enhanced understanding of the structure of weakly o-minimal models.

Abstract

We investigate the cardinality $\mathfrak n_{\dim}(\mathcal M)$ of the sets of dimension functions on weakly o-minimal structures $\mathcal M$ admitting strong cell decomposition.