Expansion of a semi-bounded o-minimal structure by a geometric progression

TL;DR

This paper shows that adding an increasing geometric progression to a semi-bounded o-minimal structure preserves local o-minimality, expanding understanding of structure stability under such expansions.

Contribution

It introduces the result that expanding semi-bounded o-minimal structures with geometric progressions maintains local o-minimality, a novel insight in model theory.

Findings

Expansion by geometric progression is locally o-minimal.

Preserves o-minimality properties under specific expansions.

Provides new tools for analyzing structure stability.

Abstract

We demonstrate that an expansion of a semi-bounded o-minimal expansion of the ordered group of reals by an increasing geometric progression is locally o-minimal.