On Amalgamation in NTP2 Theories and Generically Simple Generics

Abstract

We prove a couple of results on NTP${}_2$ theories. First, we prove an amalgamation statement and deduce from it that the Lascar distance over extension bases is bounded by $2$. This improves previous work of Ben Yaacov and Chernikov. We propose a line of investigation of NTP${}_2$ theories based on S1 ideals with amalgamation and ask some questions. We then define and study a class of groups with generically simple generics, generalizing NIP groups with generically stable generics.