| 书目名称 | Set Theory | | 副标题 | With an Introduction | | 编辑 | Abhijit Dasgupta | | 视频video | | | 概述 | Provides essential set-theoretic prerequisites for graduate work.Preserves a classical flavor by incorporating historical threads.Includes many examples of the use of set theory in topology, analysis, | | 图书封面 |  | | 描述 | .What is a number? What is infinity? What is continuity? What is order? Answers to these fundamental questions obtained by late nineteenth-century mathematicians such as Dedekind and Cantor gave birth to set theory. This textbook presents classical set theory in an intuitive but concrete manner..To allow flexibility of topic selection in courses, the book is organized into four relatively independent parts with distinct mathematical flavors. Part I begins with the Dedekind–Peano axioms and ends with the construction of the real numbers. The core Cantor–Dedekind theory of cardinals, orders, and ordinals appears in Part II. Part III focuses on the real continuum. Finally, foundational issues and formal axioms are introduced in Part IV. Each part ends with a postscript chapter discussing topics beyond the scope of the main text, ranging from philosophical remarks to glimpses into landmark results of modern set theory such as the resolution of Lusin‘s problems on projective sets using determinacy of infinite games and large cardinals..Separating the metamathematical issues into an optional fourth part at the end makes this textbook suitable for students interested in any field of mathe | | 出版日期 | Textbook 2014 | | 关键词 | Cantor‘s Theorem; Dedekind‘s Theorem; Frege; Zermelo-Fraenkel axiom system; order, cardinals, and ordina | | 版次 | 1 | | doi | https://doi.org/10.1007/978-1-4614-8854-5 | | isbn_ebook | 978-1-4614-8854-5 | | copyright | Springer Science+Business Media New York 2014 |
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发表于 2025-3-21 17:11:25
