Abstract: It is consistent that ZF + DC holds, the hypergraph of rectangles on a given Euclidean space has countable chromatic number, while the hypergraph of equilateral triangles on \mathbb{R}^2 does not.
Keywords: real algebraic geometry; algebraic hypergraph; chromatic number; geometric set theory; consistency result
DOI: DOI 10.14712/1213-7243.2023.020
AMS Subject Classification: 03E35 14P99 05C15