Coloring Isosceles Triangles in Choiceless Set Theory

Journal of Symbolic Logic:1-30 (forthcoming)
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Abstract

It is consistent relative to an inaccessible cardinal that ZF+DC holds, and the hypergraph of isosceles triangles on $\mathbb {R}^2$ has countable chromatic number while the hypergraph of isosceles triangles on $\mathbb {R}^3$ has uncountable chromatic number.

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10.1017/jsl.2023.63

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Krull dimension in set theory.Jindřich Zapletal - 2023 - Annals of Pure and Applied Logic 174 (9):103299.

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