Simplicial reformulations of equivalent characterisations of stable first order theories

I shall give simplicial reformulations of several equivalent characterisations of stability of a first order theory. In particular, I shall reformulate without any word of logic the statement of the Sela’s theorem that the theory of a free group is stable.

I will make an effort to be self-contained and remind the definitions of my previous talk. In particular, I shall define a semantics of first order formulas with respect to any simplicial set, where a predicate is assigned a subset of simplicies rather than n-tuples. From this point of view, the type space functor defined last time, is the canonical model of a first order theory.