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Pathological examples of structures with o‐minimal open core
Author(s) -
Block Gorman Alexi,
Caulfield Erin,
Hieronymi Philipp
Publication year - 2021
Publication title -
mathematical logic quarterly
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.473
H-Index - 28
eISSN - 1521-3870
pISSN - 0942-5616
DOI - 10.1002/malq.202100008
Subject(s) - unary operation , mathematics , predicate (mathematical logic) , core (optical fiber) , graph , combinatorics , discrete mathematics , computer science , programming language , telecommunications
Abstract 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.