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  1. On the classification of vertex-transitive structures.John Clemens, Samuel Coskey & Stephanie Potter - 2019 - Archive for Mathematical Logic 58 (5-6):565-574.
    We consider the classification problem for several classes of countable structures which are “vertex-transitive”, meaning that the automorphism group acts transitively on the elements. We show that the classification of countable vertex-transitive digraphs and partial orders are Borel complete. We identify the complexity of the classification of countable vertex-transitive linear orders. Finally we show that the classification of vertex-transitive countable tournaments is properly above \ in complexity.
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  • Isometry of Polish metric spaces.John D. Clemens - 2012 - Annals of Pure and Applied Logic 163 (9):1196-1209.
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  • Uncountable structures are not classifiable up to bi-embeddability.Filippo Calderoni, Heike Mildenberger & Luca Motto Ros - 2019 - Journal of Mathematical Logic 20 (1):2050001.
    Answering some of the main questions from [L. Motto Ros, The descriptive set-theoretical complexity of the embeddability relation on models of large size, Ann. Pure Appl. Logic164(12) (2013) 1454–1492], we show that whenever κ is a cardinal satisfying κ<κ=κ>ω, then the embeddability relation between κ-sized structures is strongly invariantly universal, and hence complete for (κ-)analytic quasi-orders. We also prove that in the above result we can further restrict our attention to various natural classes of structures, including (generalized) trees, graphs, or (...)
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