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Author : Frederick Rowbottom
Publisher :
ISBN 13 :
Total Pages : 164 pages
Book Rating : 4.62/5 ( download)
Download or read book Some Strong Axioms of Infinity Incompatible with the Axiom of Constructibility written by Frederick Rowbottom and published by . This book was released on 1964 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Keith J. Devlin
Publisher : Cambridge University Press
ISBN 13 : 1316739422
Total Pages : 439 pages
Book Rating : 4.26/5 ( download)
Download or read book Constructibility written by Keith J. Devlin and published by Cambridge University Press. This book was released on 2017-03-16 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their inception, the Perspectives in Logic and Lecture Notes in Logic series have published seminal works by leading logicians. Many of the original books in the series have been unavailable for years, but they are now in print once again. In this volume, the sixth publication in the Perspectives in Logic series, Keith J. Devlin gives a comprehensive account of the theory of constructible sets at an advanced level. The book provides complete coverage of the theory itself, rather than the many and diverse applications of constructibility theory, although applications are used to motivate and illustrate the theory. The book is divided into two parts: Part I (Elementary Theory) deals with the classical definition of the Lα-hierarchy of constructible sets and may be used as the basis of a graduate course on constructibility theory. and Part II (Advanced Theory) deals with the Jα-hierarchy and the Jensen 'fine-structure theory'.
Author : Alcantara
Publisher : CRC Press
ISBN 13 : 9780824773304
Total Pages : 328 pages
Book Rating : 4.06/5 ( download)
Download or read book Mathematical Logic and Formal Systems written by Alcantara and published by CRC Press. This book was released on 1985-04-25 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique collection of research papers provides an important contribution to the area of Mathematical Logic and Formal Systems. Exploring interesting practical applications as well as problems for further investigation, this single-source reference discusses the interpretations of the concept of probability and their relationship to statistical methods ... illustrates the problem of set theoretical foundations and category theory ... treats the various aspects of the theory of large cardinals including combinatorial properties of some sets naturally related to them ... resolves an open problem in the theory of relations ... and characterizes interpretations of elementary theories as functors between categories whose objects are structures. Written by world-renowned authorities in their fields, Mathematical Logic and Formal Systems is important reading for logicians, pure and applied mathematicians, and graduate students in logic courses. Book jacket.
Author : Thomas J. Jech
Publisher : American Mathematical Soc.
ISBN 13 : 0821802461
Total Pages : 232 pages
Book Rating : 4.65/5 ( download)
Download or read book Axiomatic Set Theory, Part 2 written by Thomas J. Jech and published by American Mathematical Soc.. This book was released on 1971 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michael Hallett
Publisher : Oxford University Press
ISBN 13 : 9780198532835
Total Pages : 372 pages
Book Rating : 4.30/5 ( download)
Download or read book Cantorian Set Theory and Limitation of Size written by Michael Hallett and published by Oxford University Press. This book was released on 1986 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cantor's ideas formed the basis for set theory and also for the mathematical treatment of the concept of infinity. The philosophical and heuristic framework he developed had a lasting effect on modern mathematics, and is the recurrent theme of this volume. Hallett explores Cantor's ideas and, in particular, their ramifications for Zermelo-Frankel set theory.
Author : Lev D. Beklemishev
Publisher : Elsevier
ISBN 13 : 9780080954868
Total Pages : 350 pages
Book Rating : 4.63/5 ( download)
Download or read book Provability, Computability and Reflection written by Lev D. Beklemishev and published by Elsevier. This book was released on 2000-04-01 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provability, Computability and Reflection
Author : R.L. Graham
Publisher : Elsevier
ISBN 13 : 008093384X
Total Pages : 2404 pages
Book Rating : 4.49/5 ( download)
Download or read book Handbook of Combinatorics written by R.L. Graham and published by Elsevier. This book was released on 1995-12-11 with total page 2404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Handbook of Combinatorics
Author : Thomas Jech
Publisher : Springer Science & Business Media
ISBN 13 : 3662224003
Total Pages : 642 pages
Book Rating : 4.07/5 ( download)
Download or read book Set Theory written by Thomas Jech and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 642 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main body of this book consists of 106 numbered theorems and a dozen of examples of models of set theory. A large number of additional results is given in the exercises, which are scattered throughout the text. Most exer cises are provided with an outline of proof in square brackets [ ], and the more difficult ones are indicated by an asterisk. I am greatly indebted to all those mathematicians, too numerous to men tion by name, who in their letters, preprints, handwritten notes, lectures, seminars, and many conversations over the past decade shared with me their insight into this exciting subject. XI CONTENTS Preface xi PART I SETS Chapter 1 AXIOMATIC SET THEORY I. Axioms of Set Theory I 2. Ordinal Numbers 12 3. Cardinal Numbers 22 4. Real Numbers 29 5. The Axiom of Choice 38 6. Cardinal Arithmetic 42 7. Filters and Ideals. Closed Unbounded Sets 52 8. Singular Cardinals 61 9. The Axiom of Regularity 70 Appendix: Bernays-Godel Axiomatic Set Theory 76 Chapter 2 TRANSITIVE MODELS OF SET THEORY 10. Models of Set Theory 78 II. Transitive Models of ZF 87 12. Constructible Sets 99 13. Consistency of the Axiom of Choice and the Generalized Continuum Hypothesis 108 14. The In Hierarchy of Classes, Relations, and Functions 114 15. Relative Constructibility and Ordinal Definability 126 PART II MORE SETS Chapter 3 FORCING AND GENERIC MODELS 16. Generic Models 137 17. Complete Boolean Algebras 144 18.
Author : A. R. D. Mathias
Publisher : Springer
ISBN 13 : 3540368841
Total Pages : 673 pages
Book Rating : 4.47/5 ( download)
Download or read book Cambridge Summer School in Mathematical Logic written by A. R. D. Mathias and published by Springer. This book was released on 2006-11-15 with total page 673 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : P. Erdös
Publisher : Elsevier
ISBN 13 : 0444537457
Total Pages : 349 pages
Book Rating : 4.54/5 ( download)
Download or read book Combinatorial Set Theory: Partition Relations for Cardinals written by P. Erdös and published by Elsevier. This book was released on 2011-08-18 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work presents the most important combinatorial ideas in partition calculus and discusses ordinary partition relations for cardinals without the assumption of the generalized continuum hypothesis. A separate section of the book describes the main partition symbols scattered in the literature. A chapter on the applications of the combinatorial methods in partition calculus includes a section on topology with Arhangel'skii's famous result that a first countable compact Hausdorff space has cardinality, at most continuum. Several sections on set mappings are included as well as an account of recent inequalities for cardinal powers that were obtained in the wake of Silver's breakthrough result saying that the continuum hypothesis can not first fail at a singular cardinal of uncountable cofinality.
