An o-minimalist view of the group configuration

Ya'acov Peterzil

An o-minimalist view of the group configuration

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arxiv 1909.09994 v2 pith:4UEHH2O7 submitted 2019-09-22 math.LO

Ya'acov Peterzil This is my paper · ORCID

classification math.LO

keywords groupo-minimalconfigurationdefinablytype-definableactionadditionanswer

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abstract

The group configuration in o-minimal structures gives rise, just like in the stable case, to a transitive action of a type-definable group on a partial type. Because $acl=dcl$ the o-minimal proof is significantly simpler than Hrushovski's original argument. Several equivalent versions, which are more suitable to the o-minimal setting, are formulated, in functional language and also in terms of a certain $4$-ary relation. In addition, the following question is considered: Can every definably connected type-definable group be definably embedded into a definable group of the same dimension? Two simple cases with a positive answer are given.

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Topologically 1-based T-minimal Structures
math.LO 2025-08 conditional novelty 8.0 of 10

In any non-trivial topologically 1-based t-minimal structure with independent neighborhoods, a definable open abelian topological group exists.

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