文章基本信息
- 标题：A Logical Framework for Set Theories
- 本地全文：下载
- 作者：Arnon Avron
- 期刊名称：Electronic Proceedings in Theoretical Computer Science
- 电子版ISSN：2075-2180
- 出版年度：2011
- 卷号：81
- 页码：3-15
- DOI：10.4204/EPTCS.81.1
- 出版社：Open Publishing Association
- 摘要：Axiomatic set theory is almost universally accepted as the basic theory which provides the foundations of mathematics, and in which the whole of present day mathematics can be developed. As such, it is the most natural framework for Mathematical Knowledge Management. However, in order to be used for this task it is necessary to overcome serious gaps that exist between the "official" formulations of set theory (as given e.g. by formal set theory ZF) and actual mathematical practice.
In this work we present a new unified framework for formalizations of axiomatic set theories of different strength, from rudimentary set theory to full ZF. It allows the use of set terms, but provides a static check of their validity.
