On amalgamation in NTP2 theories and generically simple generics

TL;DR

This paper advances the understanding of NTP2 theories by proving an amalgamation result, bounding Lascar distance, and exploring groups with generically simple generics, thus extending prior work in model theory.

Contribution

It introduces new amalgamation results in NTP2 theories, bounds Lascar distance over extension bases, and generalizes the concept of generically stable generics to a broader class of groups.

Findings

Lascar distance over extension bases is bounded by 2

Amalgamation results in NTP2 theories are established

Introduction of groups with generically simple generics

Abstract

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.