Some NIP-like phenomena in NTP₂

Itay Kaplan; Pierre Simon

doi:10.4171/mlm/5

BooksmlmCollected Volumepp. 171–191

Some NIP-like phenomena in NTP $_{2}$

Itay Kaplan
The Hebrew University of Jerusalem, Israel
Pierre Simon
University of California Berkeley, USA

Download Chapter PDF

A subscription is required to access this book chapter.

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 $_{2}$ .