Wild theories with o-minimal open core

Philipp Hieronymi; Travis Nell; Erik Walsberg

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arXiv · 1707.02062

Wild theories with o-minimal open core

Philipp Hieronymi·Travis Nell·Erik Walsberg

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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.

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BibTeX RIS

Philipp Hieronymi, Travis Nell, Erik Walsberg. 2017-07-07. Wild theories with o-minimal open core. https://arxiv.org/abs/1707.02062

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