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arxiv: 2508.14838 · v3 · pith:5DJLXSFHnew · submitted 2025-08-20 · 🧮 math.LO · cs.LO

Constraint satisfaction problems, compactness and non-measurable sets

Claude Tardif This is my paper
classification 🧮 math.LO cs.LO
keywords compactnessexistencefinitenon-measurablerelationalsetsstructureaxiom
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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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  1. Equivalences of promise compactness principles

    math.CO 2026-04 unverdicted novelty 8.0

    For structure pairs (A,B) without Olšák polymorphisms, the promise compactness K_(A,B) is equivalent to the ultrafilter principle over ZF, including K_(K3,K5) and K_(H2,Hc).