Set Theory : With an Introduction to Real Point Sets

種類:

電子ブック

責任表示:

by Abhijit Dasgupta

出版情報:

New York, NY : Springer New York : Imprint: Birkhäuser, 2014

著者名:

• Dasgupta, Abhijit
• SpringerLink (Online service)

ISBN:

9781461488545 [1461488540]    

注記:

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

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