Quillen Model Structures-Based Notions of Locality of Logics over Finite Models

TL;DR

This paper introduces a homotopic framework using Quillen model categories to analyze locality properties of finite logics, extending classical theorems with a new topological perspective.

Contribution

It proposes a novel homotopic approach to locality in finite model theory, based on Quillen model categories, for primitive-positive sentences of quantifier-rank k.

Findings

Develops a model category-based framework for locality

Extends classical locality theorems using homotopy theory

Provides new tools for analyzing finite model logics

Abstract

Locality is a property of logics, based on Hanf's and Gaifman's theorems, and that was shown to be very useful in the context of finite model theory. In this paper I present a homotopic variation for locality, namely a Quillen model category-based framework for locality under k-logical equivalence, for every primitive-positive sentence of quantifier-rank k.