The Joy of Sets
The Joy of Sets
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套装的乐趣
DOI：
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
K. Devlin
中科院分区：
文献类型：
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作者：
K. Devlin
这篇论文的目的是提供一个帐户的部分当代集理论是相关的其他领域的纯数学。针对高级本科生和开始研究生，文本是写在一个轻松的风格，与最低限度的形式主义。这本书以“天真”集合论的评论开始。然后，它发展了该理论的Zermelo-Fraenkel公理，展示了它们是如何自然产生的。在讨论了序数和基数之后，这本书深入研究了当代集合论，涵盖了以下主题：Borel层次结构，固定集合和回归函数，以及Lebesgue测度。两章提出了一个扩展的泽梅洛-弗兰克尔理论，讨论公理的建设性和问题的概率集理论。最后一章介绍了一个替代概念的集合论，已被证明是有用的计算机科学，非良基集理论的彼得Aczel。
This treatise is intended to provide an account of those parts of contemporary set theory that are relevant to other areas of pure mathematics. Aimed at advanced undergraduates and beginning graduate students, the text is written in an easy-going style, with a minimum of formalism. The book begins with a review of "naive" set theory. It then develops the Zermelo-Fraenkel axioms of the theory, showing how they arise naturally. After discussing the ordinal and cardinal numbers, the book then delves into contemporary set theory, covering such topics as: the Borel hierarchy, stationary sets and regressive functions, and Lebesgue measure. Two chapters present an extension of the Zermelo-Fraenkel theory, discussing the axiom of constructibility and the question of probability in set theory. A final chapter presents an account of an alternative concept of set theory that has proved useful in computer science, the non-well-founded set theory of Peter Aczel.