建构性地构建可建构宇宙

IF 0.6 2区数学 Q2 LOGIC

Annals of Pure and Applied Logic Pub Date : 2023-12-07 DOI:10.1016/j.apal.2023.103392

Richard Matthews , Michael Rathjen

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引用次数: 1

摘要

我们研究直觉主义理论的可构造宇宙 L 的性质。我们给出了一个基本运算的扩展集，它足以在直观克里普克-普拉特克集合论上生成无穷大的宇宙。在此基础上，我们研究了什么情况下 L 不能成为传统意义上的内部模型。也就是说，我们证明在构造泽梅洛-弗兰克尔（即使有幂集公理）上，我们无法证明幂级数公理在 L 中成立。

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Constructing the constructible universe constructively

We study the properties of the constructible universe, L, over intuitionistic theories. We give an extended set of fundamental operations which is sufficient to generate the universe over Intuitionistic Kripke-Platek set theory without Infinity. Following this, we investigate when L can fail to be an inner model in the traditional sense. Namely, we show that over Constructive Zermelo-Fraenkel (even with the Power Set axiom) one cannot prove that the Axiom of Exponentiation holds in L.

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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.