Monthly Archives: September 2025

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 →

This post will be updated over the course of the semester. Four people have volunteered to speak about specific topics.  The dates of their lectures will be announced later. Harper Wells will speak about the problem of the existence of … 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 →