A few more dissimilarities between second-order arithmetic and set theory

IF 0.3 4区数学 Q1 Arts and Humanities

Archive for Mathematical Logic Pub Date : 2022-07-09 DOI:10.1007/s00153-022-00829-3

Kentaro Fujimoto

引用次数: 1

Abstract

Second-order arithmetic and class theory are second-order theories of mathematical subjects of foundational importance, namely, arithmetic and set theory. Despite the similarity in appearance, there turned out to be significant mathematical dissimilarities between them. The present paper studies various principles in class theory, from such a comparative perspective between second-order arithmetic and class theory, and presents a few new dissimilarities between them.

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二阶算术与集合论的几点不同

二阶算术和类理论是数学学科中具有重要基础意义的二阶理论，即算术和集合论。尽管外表相似，但结果证明它们之间在数学上存在显著的差异。本文从二阶算法与类理论的比较角度研究了类理论中的各种原理，并提出了它们之间的一些新的不同之处。

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

Archive for Mathematical Logic MATHEMATICS-LOGIC

CiteScore

0.80

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： The journal publishes research papers and occasionally surveys or expositions on mathematical logic. Contributions are also welcomed from other related areas, such as theoretical computer science or philosophy, as long as the methods of mathematical logic play a significant role. The journal therefore addresses logicians and mathematicians, computer scientists, and philosophers who are interested in the applications of mathematical logic in their own field, as well as its interactions with other areas of research.