Lectures in Logic and Set Theory: Volume 2, Set Theory (Cambridge Studies in Advanced Mathematics)

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Lectures in Logic and Set Theory: Volume 2, Set Theory (Cambridge Studies in Advanced Mathematics)

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  • 製本 Hardcover:ハードカバー版／ページ数 592 p.
  • 言語 ENG
  • 商品コード 9780521753746
  • DDC分類 511.322

基本説明

New in paperback. Hardcover was published in 2003. Volume II, on formal (ZFC) set theory, incorporates a self-contained "chapter 0" on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques provide a solid foundation in set theory and a thorough context for the presentation of advanced topics (such as absoluteness, relative consistency results, two expositions of Godel's constructible universe, numerous ways of viewing recursion, and Cohen forcing).

Full Description

This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume II, on formal (ZFC) set theory, incorporates a self-contained 'chapter 0' on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques will provide the reader with a solid foundation in set theory and provides a context for the presentation of advanced topics such as absoluteness, relative consistency results, two expositions of Godel's constructible universe, numerous ways of viewing recursion, and a chapter on Cohen forcing.

Contents

Preface; 1. A bit of logic: a user's toolbox; 2. The set-theoretic universe, naively; 3. The axioms of set theory; 4. The axiom of choice; 5. The natural numbers; transitive closure; 6. Order; 7. Cardinality; 8. Forcing; Bibliography; List of symbols; Index.