An o-minimalist view of the group configuration

2019/09/22 by Ya’acov Peterzil, Peterzil, Ya'acov
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Logic, programming, and type systems

paper · pdf · doi:10.48550/arxiv.1909.09994

openalex publication_date 2019/09/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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