The open dihypergraph dichotomy and the second level of the Borel hierarchy
Logic
2018-03-09 v1 Combinatorics
Abstract
We show that several dichotomy theorems concerning the second level of the Borel hierarchy are special cases of the -dimensional generalization of the open graph dichotomy, which itself follows from the usual proof(s) of the perfect set theorem. Under the axiom of determinacy, we obtain the generalizations of these results from analytic metric spaces to separable metric spaces. We also consider connections between cardinal invariants and the chromatic numbers of the corresponding dihypergraphs.
Keywords
Cite
@article{arxiv.1803.03205,
title = {The open dihypergraph dichotomy and the second level of the Borel hierarchy},
author = {Raphaël Carroy and Benjamin D. Miller and Dániel T. Soukup},
journal= {arXiv preprint arXiv:1803.03205},
year = {2018}
}