Category Archives: Uncategorized

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 →

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 →

Our seminar this semester will focus on the model theory of difference fields.  We meet in 891 (note the change in location!) Evans, Wednesdays 3-4pm.  The Course Control Number is 15443.   The main sources are the following research papers. … Continue reading →

Learning seminar on o-minimality (Autumn 2024) The learning seminar on o-minimality met on Tuesdays and Thursdays, 11am-12noon in 891 Evans during the Autumn 2024 semester.  The Course Control Number was 34544. For the most part, we followed the presentation in … Continue reading →

We have two model theory seminars this semester, both of which meet in 891 Evans. The Model Theory Research Seminar meets on Wednesdays, 4-5pm and a Learning Seminar on O-minimality meets those Tuesdays and Thursdays, 11am-12noon, when I am in … Continue reading →