Constraint satisfaction problems, compactness and non-measurable sets
Logic
2026-03-09 v2 Logic in Computer Science
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.
Cite
@article{arxiv.2508.14838,
title = {Constraint satisfaction problems, compactness and non-measurable sets},
author = {Claude Tardif},
journal= {arXiv preprint arXiv:2508.14838},
year = {2026}
}
Comments
8 pages