On the classification of vertex-transitive structures

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.

References in corpus (1)

• On the classification of vertex-transitive structures

Cited by in corpus (2)

• New jump operators on equivalence relations
• On the classification of vertex-transitive structures