Pathological examples of structures with o-minimal open core

Alexi Block Gorman; Erin Caulfield; Philipp Hieronymi

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arXiv · 2101.02651

Pathological examples of structures with o-minimal open core

Alexi Block Gorman·Erin Caulfield·Philipp Hieronymi

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Abstract

This paper answers several open questions around structures with o-minimal open core. We construct an expansion of an o-minimal structure $\mathcal{R}$ by a unary predicate such that its open core is a proper o-minimal expansion of $\mathcal{R}$. We give an example of a structure that has an o-minimal open core and the exchange property, yet defines a function whose graph is dense. Finally, we produce an example of a structure that has an o-minimal open core and definable Skolem functions, but is not o-minimal.

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BibTeX RIS

Alexi Block Gorman, Erin Caulfield, Philipp Hieronymi. 2021-01-07. Pathological examples of structures with o-minimal open core. https://arxiv.org/abs/2101.02651

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