Relative geometries

Thomas Blossier (1) , Amador Martin Pizarro (1) , Frank Olaf Wagner (1)

1 ICJ - Institut Camille Jordan

We start an analysis of geometric properties of a structure relative to a reduct. In particular, we look at definability of groups and fields in this context. In the relatively one-based case, every definable group is isogenous to a subgroup of a product of groups definable in the reducts. In the relatively CM-trivial case, which contains certain Hrushovski amalgamations (the fusion of two strongly minimal sets or the expansions of a field by a predicate), every definable group allows a homomorphism with virtually central kernel into a product of groups definable in the reducts.

Mots clés: Model theory; Hrushovski Amalgamation; CM-triviality; one-based; geometry; group; definability

Domaines: Logique [math.LO]

Thomas Blossier, Amador Martin Pizarro, Frank Olaf Wagner. Relative geometries. 2011. ⟨hal-00514393v3⟩