Ernest Schimmerling

### Mathematical logic seminar - October 30, 2003

 Time: 12 - 1:20 p.m. Room: CFA 110 Speaker: Alexei Kolesnikov Graduate Student in Mathematical Sciences Carnegie Mellon University Title: On n-simplicity Abstract: I will talk about my research that was originally motivated by the question of when does a simple theory have the property of $n$-dimensional amalgamation (where 2-dimensional amalgamation corresponds to the Independence theorem for simple theories). To answer that question, I develop the notion of $n$-simplicity for $1\le n\le \omega$, where 1-simple'' is the same as simple.'' I will present the definitions and give examples of simple unstable theories in each subclass. I sketch the proofs of 3-dimensional amalgamation property for 2-simple theories, and, under an additional assumption, $(n+1)$-dimensional amalgamation property for $n$-simple theories. I will also talk about some open problems. Organizer's note: Please bring your lunch.