Indiscernible extraction and Morley sequences

This is the title of a talk given at the 2014 Logic Colloquium (Vienna University of Technology) on Jul. 19, 2014. The talk presents the corresponding paper. Here are the slides.


We present a new proof of the existence of Morley sequences in simple theories. We avoid using the Erdős-Rado theorem and instead use Ramsey's theorem. The proof shows that the basic theory of forking in simple theories can be developed inside H ((22|T|)+) without using the axiom of replacement, answering a question of Grossberg, Iovino and Lessmann, as well as a question of Baldwin.