Deciding the Chromatic Numbers of Algebraic Hypergrahs

TL;DR

This paper proves that for any infinite size, it is possible to algorithmically determine whether an algebraic hypergraph's chromatic number is at most that size.

Contribution

It establishes the decidability of the chromatic number for algebraic hypergraphs across all infinite cardinalities.

Findings

Decidability holds for all infinite cardinals.

Chromatic number bounds can be effectively determined.

Results apply to a broad class of algebraic hypergraphs.

Abstract

For each infinite cardinal k, the set of algebraic hypergraphs having chromatic number no larger than k is decidable.