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.