First-order homotopical logic

IF 0.5 3区数学 Q3 LOGIC

Journal of Symbolic Logic Pub Date : 2023-09-18 DOI:10.1017/jsl.2023.68

Joseph Helfer

引用次数: 1

Abstract

We introduce a homotopy-theoretic interpretation of intuitionistic first-order logic based on ideas from Homotopy Type Theory. We provide a categorical formulation of this interpretation using the framework of Grothendieck fibrations. We then use this formulation to prove the central property of this interpretation, namely homotopy invariance. To do this, we use the result from arXiv:1905.10690 that any Grothendieck fibration of the kind being considered can automatically be upgraded to a 2-dimensional fibration, after which the invariance property is reduced to an abstract theorem concerning pseudonatural transformations of morphisms into 2-dimensional fibrations.

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一阶同调逻辑

基于同伦类型论的思想，给出了直觉一阶逻辑的同伦解释。我们使用格罗滕迪克振动的框架提供了这种解释的分类公式。然后我们用这个公式证明了这个解释的中心性质，即同伦不变性。为了做到这一点，我们使用arXiv:1905.10690的结果，即所考虑的任何类型的Grothendieck纤维都可以自动升级为二维纤维，之后不变性性质被简化为关于态射到二维纤维的伪自然变换的抽象定理。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Symbolic Logic 数学-数学

CiteScore

1.20

自引率

16.70%

发文量

审稿时长

6-12 weeks

期刊介绍： The Journal of Symbolic Logic publishes research in mathematical logic and its applications of the highest quality. Papers are expected to exhibit innovation and not merely be minor variations on established work. They should also be of interest to a broad audience. JSL has been, since its establishment in 1936, the leading journal in the world devoted to mathematical logic. Its prestige derives from its longevity and from the standard of submissions -- which, combined with the standards of reviewing, all contribute to the fact that it receives more citations than any other journal in logic.