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arXiv · 2508.14838

Constraint satisfaction problems, compactness and non-measurable sets

Claude Tardif
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Abstract

A finite relational structure A is called compact if for any infinite relational structure B of the same type, the existence of a homomorphism from B to A is equivalent to the existence of homomorphisms from all finite substructures of B to A. We show that if A has width one, then the compactness of A can be proved in the axiom system of Zermelo and Fraenkel, but otherwise, the compactness of A implies the existence of non-measurable sets in 3-space.

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Claude Tardif. 2025-08-20. Constraint satisfaction problems, compactness and non-measurable sets. https://doi.org/10.46298/lmcs-22(3%3A1)2026

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