Wild theories with o-minimal open core

Philipp Hieronymi; Travis Nell; Erik Walsberg

doi:10.1016/j.apal.2017.10.002

Wild theories with o-minimal open core

Philipp Hieronymi, Travis Nell, Erik Walsberg

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

Let T be a consistent o-minimal theory extending the theory of densely ordered groups and let T^′ be a consistent theory. Then there is a complete theory T^⁎ extending T such that T is an open core of T^⁎, but every model of T^⁎ interprets a model of T^′. If T^′ is NIP, T^⁎ can be chosen to be NIP as well. From this we deduce the existence of an NIP expansion of the real field that has no distal expansion.

Original language	English (US)
Pages (from-to)	146-163
Number of pages	18
Journal	Annals of Pure and Applied Logic
Volume	169
Issue number	2
DOIs	https://doi.org/10.1016/j.apal.2017.10.002
State	Published - Feb 2018

Keywords

Distal
Expansions of the real line
NIP
Noiseless
O-minimal open core
Tameness

ASJC Scopus subject areas

Logic

Online availability

10.1016/j.apal.2017.10.002

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keywords = "Distal, Expansions of the real line, NIP, Noiseless, O-minimal open core, Tameness",

author = "Philipp Hieronymi and Travis Nell and Erik Walsberg",

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AU - Nell, Travis

AU - Walsberg, Erik

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AB - Let T be a consistent o-minimal theory extending the theory of densely ordered groups and let T′ be a consistent theory. Then there is a complete theory T⁎ extending T such that T is an open core of T⁎, but every model of T⁎ interprets a model of T′. If T′ is NIP, T⁎ can be chosen to be NIP as well. From this we deduce the existence of an NIP expansion of the real field that has no distal expansion.

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KW - Expansions of the real line

KW - NIP

KW - Noiseless

KW - O-minimal open core

KW - Tameness

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JO - Annals of Pure and Applied Logic

JF - Annals of Pure and Applied Logic

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Wild theories with o-minimal open core

Abstract

Keywords

ASJC Scopus subject areas

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