Arrow algebras

IF 0.8 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2026-03-01 Epub Date: 2025-10-16 DOI:10.1016/j.apal.2025.103664

Benno van den Berg, Marcus Briët

引用次数: 0

Abstract

In this paper we introduce arrow algebras, simple algebraic structures which induce elementary toposes through the tripos-to-topos construction. This includes localic toposes as well as various realizability toposes, in particular, those realizability toposes which are obtained from partial combinatory algebras. Since there are many examples of arrow algebras and arrow algebras have a number of closure properties, including a notion of subalgebra given by a nucleus, arrow algebras provide a flexible tool for constructing toposes; we illustrate this by providing some general tools for creating toposes for Kreisel's modified realizability.

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箭头代数

本文引入了箭头代数，这是一种简单的代数结构，它通过三柱到拓扑的构造推导出初等拓扑。这包括局部拓扑以及各种可实现拓扑，特别是那些由部分组合代数得到的可实现拓扑。由于箭头代数有许多例子，并且箭头代数具有许多闭包性质，包括由核给出的子代数的概念，因此箭头代数为构造拓扑提供了灵活的工具；我们通过提供一些通用工具来为Kreisel的修改可实现性创建拓扑来说明这一点。

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

Annals of Pure and Applied Logic 数学-数学

CiteScore

1.40

自引率

12.50%

发文量

审稿时长

200 days

期刊介绍： The journal Annals of Pure and Applied Logic publishes high quality papers in all areas of mathematical logic as well as applications of logic in mathematics, in theoretical computer science and in other related disciplines. All submissions to the journal should be mathematically correct, well written (preferably in English)and contain relevant new results that are of significant interest to a substantial number of logicians. The journal also considers submissions that are somewhat too long to be published by other journals while being too short to form a separate memoir provided that they are of particular outstanding quality and broad interest. In addition, Annals of Pure and Applied Logic occasionally publishes special issues of selected papers from well-chosen conferences in pure and applied logic.