TY - JOUR
T1 - Pathological Examples of Structures with O-minimal Open Core
AU - Block Gorman, Alexi
AU - Caulfield, Erin
AU - Hieronymi, Philipp
N1 - Funding Information:
Alexi Block Gorman was supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE‐1746047. Philipp Hieronymi was partially supported by NSF grant DMS‐1654725.
Funding Information:
We thank Pantelis Eleftheriou for helpful conversations on the topic of this paper, in particular for bringing Question 1 to the attention of Philipp Hieronymi at a conference at the Bedlewo Conference Center. We thank Chris Miller for helpful comments on a draft of this?paper. Alexi Block Gorman was supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-1746047. Philipp Hieronymi was partially supported by NSF grant?DMS-1654725.
Publisher Copyright:
© 2021 Wiley-VCH GmbH
PY - 2021/8
Y1 - 2021/8
N2 - This paper answers several open questions around structures with o-minimal open core. We construct an expansion of an o-minimal structure (Formula presented.) by a unary predicate such that its open core is a proper o-minimal expansion of (Formula presented.). 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.
AB - This paper answers several open questions around structures with o-minimal open core. We construct an expansion of an o-minimal structure (Formula presented.) by a unary predicate such that its open core is a proper o-minimal expansion of (Formula presented.). 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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U2 - 10.1002/malq.202100008
DO - 10.1002/malq.202100008
M3 - Article
AN - SCOPUS:85113677244
SN - 0942-5616
VL - 67
SP - 382
EP - 393
JO - Mathematical Logic Quarterly
JF - Mathematical Logic Quarterly
IS - 3
ER -