Nonstandard proof methods in toposes

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2024-02-22 DOI:10.1016/j.apal.2024.103424

José Siqueira

引用次数: 0

Abstract

We determine sufficient structure for an elementary topos to emulate Nelson's Internal Set Theory in its internal language, and show that any topos satisfying the internal axiom of choice occurs as a universe of standard objects and maps. This development allows one to employ the proof methods of nonstandard analysis (transfer, standardisation, and idealisation) in new environments such as toposes of G-sets and Boolean étendues.

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拓扑图中的非标准证明方法

我们确定了一个基本拓扑在其内部语言中模仿纳尔逊内部集合论的充分结构，并证明了任何满足内部选择公理的拓扑都是标准对象和映射的宇宙。这一发展允许我们在新的环境中使用非标准分析的证明方法（转移、标准化和理想化），如 G 集的拓扑和布尔熵。

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.