Coloring closed Noetherian graphs
Jindrich Zapletal

TL;DR
This paper investigates the coloring properties of closed Noetherian graphs within a set-theoretic framework, showing consistency results related to countable chromatic number and the non-existence of Vitali sets.
Contribution
It establishes the consistency of certain coloring properties of closed Noetherian graphs in ZF+DC set theory without assuming the Axiom of Choice.
Findings
Closed Noetherian graphs can be countably chromatic without an infinite clique.
Under ZF+DC, Vitali sets may not exist for such graphs.
The results depend on set-theoretic assumptions and are consistent with choiceless set theory.
Abstract
If G is a closed Noetherian graph on a sigma-compact Polish space without an infinite clique, it is consistent with the choiceless set theory ZF+DC that G is countably chromatic and there is no Vitali set.
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Taxonomy
TopicsAdvanced Topology and Set Theory
