Axiomatic Set Theory

G. Takeuti, W.M. Zaring (Autoren)

Buch | Hardcover

238 Seiten

1973 | 1973 ed.
Springer-Verlag New York Inc.
978-0-387-90051-3 (ISBN)

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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.

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.

Erscheint lt. Verlag	6.4.1973
Reihe/Serie	Graduate Texts in Mathematics ; 8
Zusatzinfo	biography
Verlagsort	New York, NY
Sprache	englisch
Gewicht	450 g
Einbandart	Leinen
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
Themenwelt	Mathematik / Informatik ► Mathematik ► Logik / Mengenlehre
ISBN-10	0-387-90051-9 / 0387900519
ISBN-13	978-0-387-90051-3 / 9780387900513
Zustand	Neuware