Axiom of choice and chromatic number of the plane

by Shelah and Soifer. [ShSf:E33]
Jornal Combinatorial Theory, Series A, 2003
We will present here an example of a distance graph on the line R, whose chromatic number depends a great deal upon the axiom of choice. While the setting of our example differs from that of chromatic number of the plane problem, the example illuminates how the value of chromatic number may be affected by inclusion or exclusion of the axiom of choice in the system of axioms for sets.


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