Relative Geometric Configurations
نویسنده
چکیده
This is a survey of a recent work done by the three authors, in which an analysis of geometric properties of a structure relative to a reduct is initiated. In particular, definable groups and fields in this context are considered. In a relatively 1-based theory every group is definably isogenous to a subgroup of a group definable in the reduct. For relatively CM-trivial theories (which encompass certain Hrushovski’s amalgams, such as the fusion of two strongly minimal theories or coloured fields), we prove that every group can be mapped by a homomorphism with central kernel to a group definable in the reduct.
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