Relativizing Operational Set Theory

IF 0.7 3区数学 Q1 LOGIC

Bulletin of Symbolic Logic Pub Date : 2016-09-01 DOI:10.1017/BSL.2016.11

Gerhard Jäger

引用次数: 2

Abstract

We introduce a way of relativizing operational set theory that also takes care of application. After presenting the basic approach and proving some essential properties of this new form of relativization we turn to the notion of relativized regularity and to the system OST (LR) that extends OST by a limit axiom claiming that any set is element of a relativized regular set. Finally we show that OST (LR) is proof-theoretically equivalent to the well-known theory KPi for a recursively inaccessible universe.

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相对化操作集理论

我们引入了一种相对化操作集理论的方法，同时也考虑了它的应用。在给出了这种新形式的相对论的基本方法和证明了一些基本性质之后，我们转向了相对正则性的概念和系统OST (LR)，该系统通过一个极限公理来扩展OST，该公理宣称任何集合都是相对正则集的元素。最后，我们证明了OST (LR)在理论上与众所周知的递归不可达宇宙的理论KPi是等价的。

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

Bulletin of Symbolic Logic 数学-数学

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Bulletin of Symbolic Logic was established in 1995 by the Association for Symbolic Logic to provide a journal of high standards that would be both accessible and of interest to as wide an audience as possible. It is designed to cover all areas within the purview of the ASL: mathematical logic and its applications, philosophical and non-classical logic and its applications, history and philosophy of logic, and philosophy and methodology of mathematics.