On the Classification of Vertex-Transitive Structures

Authors

John Clemens, Boise State UniversityFollow
Samuel Coskey, Boise State UniversityFollow
Stephanie Potter, Boise State University

Document Type

Article

Publication Date

8-2019

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 E₀ in complexity.

Copyright Statement

This is a post-peer-review, pre-copyedit version of an article published in Archive for Mathematical Logic. The final authenticated version is available online at doi: 10.1007/s00153-018-0651-2

Publication Information

Clemens, John; Coskey, Samuel; and Potter, Stephanie. (2019). "On the Classification of Vertex-Transitive Structures". Archive for Mathematical Logic, 58(5-6), 565-574. https://doi.org/10.1007/s00153-018-0651-2