On the Classification of Vertex-Transitive Structures

John Clemens, Samuel Coskey, Stephanie Potter

Research output: Contribution to journalArticlepeer-review

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. (This is sometimes called homogeneous.) 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 E 0 in complexity.

Original languageAmerican English
JournalMathematics Faculty Publications and Presentations
StatePublished - 1 Aug 2019

Keywords

  • Borel complexity theory
  • graphs
  • linear orders
  • tournaments

EGS Disciplines

  • Mathematics

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