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Keywords:
real algebraic geometry; algebraic hypergraph; chromatic number; geometric set theory; consistency result
real algebraic geometry; algebraic hypergraph; chromatic number; geometric set theory; consistency result
Summary:
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.
References:
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