大基数公理是限制性的吗?

IF 0.8 1区哲学 Q2 HISTORY & PHILOSOPHY OF SCIENCE

Philosophia Mathematica Pub Date : 2023-09-24 DOI:10.1093/philmat/nkad014

Neil Barton

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引用次数: 0

摘要

摘要集合论中的独立性现象虽然普遍存在，但可以通过使用大基数公理来部分地解决。一个普遍假设的想法是，大基本公理是极大性原则的一种。在本文中，我对这种说法提出了质疑。我证明了存在一种极大性(即绝对性)，在此基础上，相对于限制性的正式概念，大的基本公理是限制性的。在这个框架内，我认为大基本公理仍然可以发挥许多通常的基础作用。

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Are Large Cardinal Axioms Restrictive?

Abstract The independence phenomenon in set theory, while pervasive, can be partially addressed through the use of large cardinal axioms. A commonly assumed idea is that large cardinal axioms are species of maximality principles. In this paper I question this claim. I show that there is a kind of maximality (namely absoluteness) on which large cardinal axioms come out as restrictive relative to a formal notion of restrictiveness. Within this framework, I argue that large cardinal axioms can still play many of their usual foundational roles.

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来源期刊

Philosophia Mathematica HISTORY & PHILOSOPHY OF SCIENCE-

CiteScore

1.70

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： Philosophia Mathematica is the only journal in the world devoted specifically to philosophy of mathematics. The journal publishes peer-reviewed new work in philosophy of mathematics, the application of mathematics, and computing. In addition to main articles, sometimes grouped on a single theme, there are shorter discussion notes, letters, and book reviews. The journal is published online-only, with three issues published per year.