A sufficient condition for first order non-definability of arrowing problems

TL;DR

This paper provides a sufficient condition, based on finite model theory and combinatorics, for when arrowing problems cannot be defined in first-order logic, advancing understanding of their logical complexity.

Contribution

It introduces a new sufficient condition for non-definability of arrowing problems in first-order logic using Hanf's Theorem and combinatorial concepts.

Findings

Identifies a sufficient condition for non-definability in first-order logic

Utilizes Hanf's Theorem and combinatorial tools like senders and determiners

Advances theoretical understanding of arrowing problems' logical limits

Abstract

We here present a sufficient condition for general arrowing problems to be non definable in first order logic, based in well known tools of finite model theory e.g. Hanf's Theorem and known concepts in finite combinatorics, like senders and determiners.