Scholarlink

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 et al. (Ordered graph limits and their applications. In: Lee, J.R. (ed.) 12th Innovations in Theoretical Computer Science Conference, ITCS 2021, January 6–8, 2021, Virtual Conference. LIPIcs, vol. 185, pp. 42:1–42:20. Schloss Dagstuhl-Leibniz-Zentrum für Informatik (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.

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Pixelating Relations and Functions Without Adding Substructures

  • 章节

  • 发表日期：

    2025年

查看全文
  • Eldar Fischer

摘要

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 et al. (Ordered graph limits and their applications. In: Lee, J.R. (ed.) 12th Innovations in Theoretical Computer Science Conference, ITCS 2021, January 6–8, 2021, Virtual Conference. LIPIcs, vol. 185, pp. 42:1–42:20. Schloss Dagstuhl-Leibniz-Zentrum für Informatik (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.