Axiomatic Set Theory / by G. Takeuti, W.M. Zaring.

Format:

Book

Author/Creator:

Takeuti, G., author.

Zaring, W.M., author.

Contributor:

SpringerLink (Online service)

Series:

Graduate texts in mathematics 2197-5612 ; 8.

Graduate Texts in Mathematics, 2197-5612 ; 8

Language:

English

Subjects (All):

Logic, Symbolic and mathematical.

Mathematical Logic and Foundations.

Local Subjects:

Mathematical Logic and Foundations.

Physical Description:

1 online resource (238 pages).

Edition:

First edition 1973.

Contained In:

Springer Nature eBook

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 1973.

System Details:

text file PDF

Summary:

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.

Contents:

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.

Other Format:

Printed edition:

ISBN:

9781468487510

Access Restriction:

Restricted for use by site license.