Pseudo real closed field, pseudo p-adically closed fields and NTP2

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.

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• Notes on trace equivalence
• Immediately algebraically closed fields