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Preprint Number 1398

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1398. Alexander Berenstein, Juan Felipe Carmona, Evgueni Vassiliev
Supersimple structures with a dense independent subset

Submission date: 20 March 2018


Based on the work done in [BV-Tind,DMS] in the o-minimal and geometric settings, we study expansions of models of a supersimple theory with a new predicate distiguishing a set of forking-independent elements that is dense inside a partial type G(x), which we call H-structures. We show that any two such expansions have the same theory and that under some technical conditions, the saturated models of this common theory are again H-structures. We prove that under these assumptions 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, when T has SU-rank ω^α and the SU-rank is continuous, we take G(x) to be the type of elements of SU-rank ω^α and we describe a natural “geometry of generics modulo H” associated with such expansions and show it is modular.

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Full text arXiv 1803.07215: pdf, ps.

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