Implications of a Quillen Model Structures-Based Framework for Locality under Logical Equivalence

TL;DR

This paper explores the implications of a homotopy-theoretic framework based on Quillen model categories for understanding locality in logic under logical equivalence, extending previous work on primitive-positive sentences.

Contribution

It introduces a new framework using Quillen model structures to analyze locality in logic, providing insights and potential directions for future research.

Findings

Framework connects homotopy theory with logical locality.

Implications for primitive-positive sentences of quantifier-rank k.

Suggests new avenues for investigating logical properties.

Abstract

In [15] a homotopic variation for locality of logics was presented, namely a Quillen model category-based framework for locality under logical equivalence, for every primitive-positive sentence of quantifier-rank $k$. In this paper, we will present some of the implications and possible themes for investigations that arise from the aforementioned framework.