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

Itay Kaplan; Pierre Simon

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arXiv · 1707.05087

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

Itay Kaplan·Pierre Simon

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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$_{2}$.

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BibTeX RIS

Itay Kaplan, Pierre Simon. 2017-07-17. Some NIP-like phenomena in NTP$_{2}$. https://arxiv.org/abs/1707.05087

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