A complexity problem for Borel graphs - Sorbonne Université
Article Dans Une Revue Inventiones Mathematicae Année : 2021

A complexity problem for Borel graphs

Résumé

We show that there is no simple (e.g. finite or countable) basis for Borel graphs with infinite Borel chromatic number. In fact, it is proved that the closed subgraphs of the shift graph on [N]N with finite (or, equivalently, ≤3) Borel chromatic number form a ΣΣ12-complete set. This answers a question of Kechris and Marks and strengthens several earlier results.
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Dates et versions

hal-03235782 , version 1 (26-05-2021)

Identifiants

Citer

Stevo Todorčević, Zoltán Vidnyánszky. A complexity problem for Borel graphs. Inventiones Mathematicae, 2021, 226, pp.225 - 249. ⟨10.1007/s00222-021-01047-z⟩. ⟨hal-03235782⟩
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