Pseudo real closed field, pseudo p-adically closed fields and NTP2
Logic
2016-10-12 v2
Abstract
The main result of this paper is a positive answer to the Conjecture 5.1 by A. Chernikov, I. Kaplan and P. Simon: If M is a PRC field, then Th(M) is NTP_2 if and only if M is bounded. In the case of PpC fields, we prove that if M is a bounded PpC field, then Th(M) is NTP_2. We also generalize this result to obtain that, if M is a bounded PRC or PpC field with exactly n orders or p-adic valuations respectively, then Th(M) is strong of burden n. This also allows us to explicitly compute the burden of types, and to describe forking.
Keywords
Cite
@article{arxiv.1411.7654,
title = {Pseudo real closed field, pseudo p-adically closed fields and NTP2},
author = {Samaria Montenegro},
journal= {arXiv preprint arXiv:1411.7654},
year = {2016}
}