| Thursday 18 April 2024 | |
| Events for day: Wednesday 16 December 2020 |
| 16:30 - 18:30 Mathtematical Logic Weekly Seminar Universal Theories and Compactly Expandable Models School MATHEMATICS Let $M$ be structure of cardinality $kappa$ with language $ au(M)leqkappa$. We say that is extit{compactly expandable} if for every theory $T$ of language $ au(T)$ with $ au(M)subseteq au(T)$ and $|T|leqkappa$ can be realised in an expansion of $M$, whenever every finite subset of $T$ can be realised in an expansion of $M$. We say that $M$ is extit{expandable} if the requirement of finite satisfiability can be weakened to: $T$ is consistent with the complete theory Th$(M)$ of $M$. Clearly, expandable models are compactly expandable. The existence of a compactly expandable model which is not expandable was conjectured in cite{95} and has b ... |