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 language | American English |
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Journal | Mathematics Faculty Publications and Presentations |
State | Published - 1 Aug 2019 |
Keywords
- Borel complexity theory
- graphs
- linear orders
- tournaments
EGS Disciplines
- Mathematics