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  1. Forking, imaginaries, and other features of.Christian D’elbée - 2021 - Journal of Symbolic Logic 86 (2):669-700.
    We study the generic theory of algebraically closed fields of fixed positive characteristic with a predicate for an additive subgroup, called $\mathrm {ACFG}$. This theory was introduced in [16] as a new example of $\mathrm {NSOP}_{1}$ nonsimple theory. In this paper we describe more features of $\mathrm {ACFG}$, such as imaginaries. We also study various independence relations in $\mathrm {ACFG}$, such as Kim-independence or forking independence, and describe interactions between them.
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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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