Pathological examples of structures with o‐minimal open core

Pathological examples of structures with o‐minimal open core

This paper answers several open questions around structures with o‐minimal open core. We construct an expansion of an o‐minimal structure R by a unary predicate such that its open core is a proper o‐minimal expansion of R. We give an example of a structure that has an o‐minimal open core and the exc...

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Veröffentlicht in:Mathematical logic quarterly 2021-08, Vol.67 (3), p.382-393
Hauptverfasser: Block Gorman, Alexi, Caulfield, Erin, Hieronymi, Philipp
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container_title Mathematical logic quarterly
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creator Block Gorman, Alexi
Caulfield, Erin
Hieronymi, Philipp
description This paper answers several open questions around structures with o‐minimal open core. We construct an expansion of an o‐minimal structure R by a unary predicate such that its open core is a proper o‐minimal expansion of 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.
doi_str_mv 10.1002/malq.202100008
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title Pathological examples of structures with o‐minimal open core
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