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

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

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.

Sheafifiable homotopy model categories

If a Quillen model category can be specified using a certain logical syntax (intuitively, ``is algebraic/combinatorial enough''), so that it can be defined in any category of sheaves, then the satisfaction of Quillen's axioms over any site is a purely formal consequence of their being satisfied over the category of sets. Such data give rise to a functor from the category of topoi and geometric morphisms to Quillen model categories and Quillen adjunctions.

隧道几何与增殖逻辑：一种严格的范畴等价

Tunnel Geometry and Proliferation Logic: A Strict Categorical Equivalence

本文通过严格范畴等价证明隧道几何与增殖逻辑在结构描述上本质相同，揭示二者为同一静态本体论的两个方面。