Relative geometries
Logic
2013-05-22 v4
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.
Cite
@article{arxiv.1009.0367,
title = {Relative geometries},
author = {Thomas Blossier and Amador Martin Pizarro and Frank Olaf Wagner},
journal= {arXiv preprint arXiv:1009.0367},
year = {2013}
}