On the classification of vertex-transitive structures

Archive for Mathematical Logic 58 (5-6):565-574 (2019)
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Abstract

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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Citations of this work

New jump operators on equivalence relations.John D. Clemens & Samuel Coskey - 2022 - Journal of Mathematical Logic 22 (3).

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References found in this work

Infinite time Turing machines.Joel David Hamkins & Andy Lewis - 2000 - Journal of Symbolic Logic 65 (2):567-604.
An absoluteness principle for borel sets.Greg Hjorth - 1998 - Journal of Symbolic Logic 63 (2):663-693.
Isomorphism of Homogeneous Structures.John D. Clemens - 2009 - Notre Dame Journal of Formal Logic 50 (1):1-22.
Invariant descriptive set theory. Pure and applied mathematics.Su Gao - 2011 - Bulletin of Symbolic Logic 17 (2):265-267.

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