Article
On the Classification of Vertex-Transitive Structures
Archive for Mathematical Logic
Document Type
Article
Publication Date
8-1-2019
Disciplines
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
Citation Information
John Clemens, Samuel Coskey and Stephanie Potter. "On the Classification of Vertex-Transitive Structures" Archive for Mathematical Logic (2019) Available at: http://works.bepress.com/john-clemens/10/