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NTP_2 groups with f-generics and PRC fields Montenegro, Samaria


This is a joint work with Alf Onshuus and Pierre Simon. In this talk we focus on groups with f-generic types definable in NTP2 theories. In particular we study the case of bounded PRC fields. PRC fields were introduced by Prestel and Basarav as a generalization of real closed fields and pseudo algebraically closed fields, where we admit having several orders. We know that the complete theory of a bounded PRC field is NTP2 and we have a good description of forking. We use some alternative versions of Hrushovskiâ s â Stabilizer Theoremâ to describe the definable groups with f generics in PRC fields. The main theorem is that such a group is isogeneous with a finite index subgroup of a quantifier-free definable groups. In fact, the latter group admits a definable covering by multi-cells on which the group operation is algebraic. This generalizes similar results proved by Hrushovski and Pillay for (not necessarily f-generic) groups definable in both pseudo finite fields and real closed fields.

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