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Preprint Number 848

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848. Alexander Berenstein, Juan Felipe Carmona, Evgueni Vassiliev
Supersimple structures with a dense independent subset (Former title: Structures of SU-rank omega with a dense independent subset of generics)
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Submission date: 18 March 2015. Revised: 3 January 2018.

Abstract:

Extending the work done in [5,9] in the o-minimal and geometric settings, we study expansions of models of a supersimple theory of SU-rank ω with a “dense codense” independent collection H of elements of rank ω, where density of H means it intersects any definable set of SU-rank ω. We show that under some technical conditions, the class of such structures is first order. We prove that the expansion is supersimple and characterize forking and canonical bases of types in the expansion. We also analyze the effect these expansions have on one-basedness and CM-triviality. In the one-based case, we describe a natural “geometry of generics modulo H” associated with such expansions and show it is modular.

Mathematics Subject Classification: 03C45

Keywords and phrases: supersimple theories, SU-rank omega, unary predicate expansions, one-basedness, ampleness, CM-triviality

Full text: pdf. (Version of 18 March 2015: pdf, dvi, ps).


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