Submission date: 17 July 2017

Abstract:

We introduce the notion of an NTP_{2}-smooth measure and prove that they exist assuming NTP_{2}. Using this, we propose a notion of distality in NTP_{2} that unfortunately does not intersect simple theories trivially. We then prove a finite alternation theorem for a subclass of NTP_{2} that contains resilient theories. In the last section we prove that under NIP, any type over a model of singular size is finitely satisfiable in a smaller model, and ask if a parallel result (with non-forking replacing finite satisfiability) holds in NTP_{2}.

Mathematics Subject Classification: 03C45, 03C95, 03C55

Keywords and phrases:

Full text arXiv 1707.05087: pdf, ps.