Author Archives: scanlon

Title: Where to look for tensor categories in model theory? Abstract: I will review recent constructions of oligomorphic tensor categories generalizing Deligne’s $\operatorname{Rep}(S_t)$ from a model theoretic point of view. Then, I will explain where there are no continuous families like … Continue reading →

On Wednesday, March 11th, 2026, Zixuan Zhu, visiting from Universität Münster by way of Notre Dame, will be speaking in our seminar.  The title and abstract follow.   Title: Rank and Independence of Imaginaries in Proper Pairs of ACF Abstract: … Continue reading →

Let $T$ be a theory with a good notion of independence.  Generally, we have in mind forking independence, though something weaker would be acceptable.  In fact, for our proof, the only properties we use are that independence is invariant under … Continue reading →

Our proof of model completeness for ACFA yields  strong quantifier simplification results. Let us start with a relative completeness result.   If a theory $T$ is model complete, then whenever $E \models T$ and $E \subseteq M_i \models T$ for $i … Continue reading →

The theory of difference fields admits a model companion, ACFA, often called “algebraically closed fields with a generic automorphism”.    To prove this, we need to show that the class of existentially closed difference fields is first-order axiomatizable. We have … Continue reading →

Before we get to the scientfic content, allow me to remind you that the location for the seminar has changed to 891 Evans and we meet Wednesdays, 3-4pm.   Definition:  A difference field $(K,\sigma)$ is a field given together with … Continue reading →