We prove a couple of results on NTP theories. First, we prove an amalgamation statement and deduce from it that the Lascar distance over extension bases is bounded by . This improves previous work of Ben Yaacov and Chernikov. We propose a line of investigation of NTP 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.
"On Amalgamation in NTP Theories and Generically Simple Generics." Notre Dame J. Formal Logic 61 (2) 233 - 243, May 2020. https://doi.org/10.1215/00294527-2020-0003