  We prove a couple of results on NTP2 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 NTP2 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.

Logic