Pixelating Relations and Functions Without Adding Substructures
Logic
2024-02-06 v3 Combinatorics
Abstract
We investigate models of relations over a bounded continuous segment of real numbers, along with the natural linear order over the reals being provided as a "hard-coded" relation. This paper presents a generalization of a lemma from [Ben-Eliezer, Fischer, Levi and Yoshida, ITCS 2021], showing that with a small amount of modification (measured in terms of the Lebesgue measure) we can replace such a model with a "pixelated" one that has a finite description, in a way that preserves all universally quantified statements over the relations, or in other words, without adding any new substructures.
Cite
@article{arxiv.2401.08082,
title = {Pixelating Relations and Functions Without Adding Substructures},
author = {Eldar Fischer},
journal= {arXiv preprint arXiv:2401.08082},
year = {2024}
}
Comments
15 pages. R1: corrected a few typos and expanded the "Discussion and variants" section. R2: more typos