Simple product and locally o-minimal theories

Abstract

There exist NIP and non-NTP${}_2$ theories satisfying all the following conditions: It is not o-minimal; All models are strongly locally o-minimal; It has a model which is an expansion of the linearly ordered abelian group over the reals $(\mathbb{R};0,+,<)$. We construct these examples using the notion of simple product.

Corrected based on the comment from John Goodrick

References in corpus (1)

• Uniform local definable cell decomposition for locally o-minimal expansion of the group of reals