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

The main result of this paper is a positive answer to the Conjecture 5.1 of [14] by A. Chernikov, I. Kaplan and P. Simon: If M   is a PRC field, then Th(M)Th(M) is NTP2 if and only if M is bounded. In the case of PpC fields, we prove that if M is a bounded Pp  C field, then Th(M)Th(M) is NTP2. 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)Th(M) is strong of burden n. This also allows us to explicitly compute the burden of types, and to describe forking.