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Seminar

Berkeley Model Theory Seminar: Pseudo Real Closed fields and NTP2 April 16, 2014 (02:00 PM PDT - 03:00 PM PDT)
Parent Program: Model Theory, Arithmetic Geometry and Number Theory
Location: MSRI: Simons Auditorium
Speaker(s) Samaria Montenegro-Guzman (Université de Paris VII (Denis Diderot))
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The notion of PAC fields has been generalized by Basarab and by Prestel to ordered fields. Prestel defines a field M to be Pseudo Real Closed field (PRC) if M is existentially closed (in the language of rings) in every regular extension L to which all orderings of M extend. Equivalently, if every absolutely irreducible variety defined over M that has a rational point in every real closure of M, has an M-rational point.

In the first part of the talk I will present a short summary of the required preliminaries on pseudo real closed fields.The main theorem is a positive answer to the conjecture by A. Chernikov, I. Kaplan and P. Simon: If M is a PRC field, then Th(M) is NTP2 if and only if M is bounded.

In the second part of the talk I will give a sketch of the proof.

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