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arXiv · 1009.0367

Relative geometries

Thomas Blossier·Amador Martin Pizarro·Frank Olaf Wagner
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Abstract

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.

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Thomas Blossier, Amador Martin Pizarro, Frank Olaf Wagner. 2010-09-02. Relative geometries. https://arxiv.org/abs/1009.0367

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