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  1. Products of Classes of Finite Structures.Vince Guingona, Miriam Parnes & Lynn Scow - 2023 - Notre Dame Journal of Formal Logic 64 (4):441-469.
    We study the preservation of certain properties under products of classes of finite structures. In particular, we examine indivisibility, definable self-similarity, the amalgamation property, and the disjoint n-amalgamation property. We explore how each of these properties interacts with the lexicographic product, full product, and free superposition of classes of structures. Additionally, we consider the classes of theories which admit configurations indexed by these products. In particular, we show that, under mild assumptions, the products considered in this article do not yield (...)
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  • Omega-Categorical Pseudofinite Groups.Dugald Macpherson & Katrin Tent - forthcoming - Journal of Symbolic Logic:1-14.
    We explore the interplay between $\omega $ -categoricity and pseudofiniteness for groups, and we conjecture that $\omega $ -categorical pseudofinite groups are finite-by-abelian-by-finite. We show that the conjecture reduces to nilpotent p-groups of class 2, and give a proof that several of the known examples of $\omega $ -categorical p-groups satisfy the conjecture. In particular, we show by a direct counting argument that for any odd prime p the ( $\omega $ -categorical) model companion of the theory of nilpotent class (...)
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