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  1. Supersimple structures with a dense independent subset.Alexander Berenstein, Juan Felipe Carmona & Evgueni Vassiliev - 2017 - Mathematical Logic Quarterly 63 (6):552-573.
    Based on the work done in [][] 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, 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 (...)
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  • Towards a finer classification of strongly minimal sets.John T. Baldwin & Viktor V. Verbovskiy - 2024 - Annals of Pure and Applied Logic 175 (2):103376.
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  • Strongly minimal Steiner systems I: Existence.John Baldwin & Gianluca Paolini - 2021 - Journal of Symbolic Logic 86 (4):1486-1507.
    A linear space is a system of points and lines such that any two distinct points determine a unique line; a Steiner k-system is a linear space such that each line has size exactly k. Clearly, as a two-sorted structure, no linear space can be strongly minimal. We formulate linear spaces in a vocabulary $\tau $ with a single ternary relation R. We prove that for every integer k there exist $2^{\aleph _0}$ -many integer valued functions $\mu $ such that (...)
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