Model Theory of Pseudo Real Closed Fields

Abstract: The notion of PAC field has been generalized by S. Basarab and by A. Prestel to ordered fields. Prestel calls a field M pseudo real closed (PRC) if M is existentially closed in every regular extension L to which all orderings of M extend. Thus PRC fields are to real closed fields what PAC fields are to algebraically closed fields. In this talk we will study the class of pseudo real closed fields (PRC-fields) from a model theoretical point of view and we will explain some of the main results obtained. We know that the complete theory of a bounded PRC field (i.e., with finitely many algebraic extensions of degree m, for each m > 1) is NTP_2 and we have a good description of forking.

Also, in a joint work with Alf Onshuus and Pierre Simon we describe the definable groups in the case that they have f-generics types.

In the end of the talk we will explain some results obtained with Silvain Rideau. Where we generalize the notion of PRC fields to a more general class of fields. In particular, this class includes fields that have orders and valuations at the same time.

commutative algebralogic

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic