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Preprint Number 1650

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1650. Ya'acov Peterzil
An o-minimalist view of the group configuration

Submission date: 22 September 2019


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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Full text arXiv 1909.09994: pdf, ps.

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