English

Krull dimension in set theory

Logic 2021-08-24 v1

Abstract

Let n>1 be a number. Let Gn be the hypergraph of all rectangles in an n-dimensional Euclidean space. It is consistent that ZF+DC holds, the chromatic number of Gn is countable, yet the chromatic number of Gn+1 is uncountable.

Keywords

Cite

@article{arxiv.2108.09850,
  title  = {Krull dimension in set theory},
  author = {Jindrich Zapletal},
  journal= {arXiv preprint arXiv:2108.09850},
  year   = {2021}
}
R2 v1 2026-06-24T05:19:43.798Z