Wild theories with o-minimal open core

Philipp Hieronymi, Travis Nell, Erik Walsberg

Published 2017-07-07Version 1

Let $T$ be a complete o-minimal theory extending the theory of densely ordered groups and let $T'$ be any theory. Then there is a theory $T^*$ that has $T$ as its open core, but all of its models interpret 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.