2007 seminar talk: A gentle introduction to non-structure of submodels of a large unstable homogeneous model, Part II

Talk held by Agatha Walczak-Typke (KGRC) at the KGRC seminar on 2007-06-14.

Abstract

The work presented is joint with S-D Friedman and T Hyttinen. We aim to generalize a very nice result of Friedman, Hyttinen, and Rautila, which ties first-order model theoretic classification theory to constructibility under the assumption of 0#, to a non-elementary model theoretic setting. The orignal result stated:

Theorem. Assume 0# exists and let T be a constructible first-orer theory which is countable in the constructible universe L. Let \kappa be a cardinal in L larger than (\aleph_1)^L. Then the collection of constructible pairs of models A,B of T, |A|,|B|=\kappa, which are isomorphic in a cardinal- and real-preserving extension of L is itself constructible if and only if T is classifiable (i.e. superstable with NDOP and NOTOP).

We have chosen Homogeneous Model Theory as a good setting for generalizing this result.

In Part I of this talk, a gentle introduction to Homogeneous Model Theory was given, as well as a justification as to why this is a good setting to choose.

In Part II, one easy step for our generalization will be sketched: the unstable case.