Axiomatic Set Theory / by Gaisi Takeuti, Wilson M. Zaring
(Graduate Texts in Mathematics ; 8)
| データ種別 | 電子ブック |
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| 出版者 | New York, NY : Springer New York |
| 出版年 | 1973 |
| 本文言語 | 英語 |
| 大きさ | 238 p : online resource |
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| 内容注記 | 1. Boolean Algebra 2. Generic Sets 3. Boolean ?-Algebras 4. Distributive Laws 5. Partial Order Structures and Topological Spaces 6. Boolean-Valued Structures 7. Relative Constructibility 8. Relative Constructibility and Ramified Languages 9. Boolean-Valued Relative Constructibility 10. Forcing 11. The Independence of V = L and the CH 12. independence of the AC 13. Boolean-Valued Set Theory 14. Another Interpretation of V(B) 15. An Elementary Embedding of V[F0] in V(B) 16. The Maximum Principle 17. Cardinals in V(B) 18. Model Theoretic Consequences of the Distributive Laws 19. Independence Results Using the Models V(B) 20. Weak Distributive Laws 21. A Proof of Marczewski’s Theorem 22. The Completion of a Boolean Algebra 23. Boolean Algebras that are not Sets 24. Easton’s Model Problem List Index of Symbols |
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| 一般注記 | This text deals with three basic techniques for constructing models of Zermelo-Fraenkel set theory: relative constructibility, Cohen's forcing, and Scott-Solovay's method of Boolean valued models. Our main concern will be the development of a unified theory that encompasses these techniques in one comprehensive framework. Consequently we will focus on certain funda mental and intrinsic relations between these methods of model construction. Extensive applications will not be treated here. This text is a continuation of our book, "I ntroduction to Axiomatic Set Theory," Springer-Verlag, 1971; indeed the two texts were originally planned as a single volume. The content of this volume is essentially that of a course taught by the first author at the University of Illinois in the spring of 1969. From the first author's lectures, a first draft was prepared by Klaus Gloede with the assistance of Donald Pelletier and the second author. This draft was then rcvised by the first author assisted by Hisao Tanaka. The introductory material was prepared by the second author who was also responsible for the general style of exposition throughout the text. We have inc1uded in the introductory material al1 the results from Boolean algebra and topology that we need. When notation from our first volume is introduced, it is accompanied with a deflnition, usually in a footnote. Consequently a reader who is familiar with elementary set theory will find this text quite self-contained |
| 著者標目 | *Takeuti, Gaisi author Zaring, Wilson M. author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Mathematical logic FREE:Mathematics FREE:Mathematical Logic and Foundations |
| 分 類 | DC23:511.3 |
| 巻冊次 | ISBN:9781468487510 
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| ISBN | 9781468487510 |
| URL | http://dx.doi.org/10.1007/978-1-4684-8751-0 |
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