## Set Theory And The Continuum Hypothesis

**Author**: Paul J. Cohen

**Editor:**Courier Corporation

**ISBN:**0486469212

**Size**: 14,34 MB

**Format:**PDF, ePub

**Read:**599

This exploration of a notorious mathematical problem is the work of the man who discovered the solution. Written by an award-winning professor at Stanford University, it employs intuitive explanations as well as detailed mathematical proofs in a self-contained treatment. This unique text and reference is suitable for students and professionals. 1966 edition. Copyright renewed 1994.

## The Consistency Of The Axiom Of Choice And Of The Generalized Continuum Hypothesis With The Axioms Of Set Theory

**Author**: Kurt G?del

**Editor:**Princeton University Press

**ISBN:**9780691079271

**Size**: 14,18 MB

**Format:**PDF, Mobi

**Read:**913

Kurt Gödel, mathematician and logician, was one of the most influential thinkers of the twentieth century. Gödel fled Nazi Germany, fearing for his Jewish wife and fed up with Nazi interference in the affairs of the mathematics institute at the University of Göttingen. In 1933 he settled at the Institute for Advanced Study in Princeton, where he joined the group of world-famous mathematicians who made up its original faculty. His 1940 book, better known by its short title, The Consistency of the Continuum Hypothesis, is a classic of modern mathematics. The continuum hypothesis, introduced by mathematician George Cantor in 1877, states that there is no set of numbers between the integers and real numbers. It was later included as the first of mathematician David Hilbert's twenty-three unsolved math problems, famously delivered as a manifesto to the field of mathematics at the International Congress of Mathematicians in Paris in 1900. In The Consistency of the Continuum Hypothesis Gödel set forth his proof for this problem. In 1999, Time magazine ranked him higher than fellow scientists Edwin Hubble, Enrico Fermi, John Maynard Keynes, James Watson, Francis Crick, and Jonas Salk. He is most renowned for his proof in 1931 of the 'incompleteness theorem,' in which he demonstrated that there are problems that cannot be solved by any set of rules or procedures. His proof wrought fruitful havoc in mathematics, logic, and beyond.

## Set Theory And The Continuum Problem

**Author**: Raymond M. Smullyan

**Editor:**

**ISBN:**9780486474847

**Size**: 17,53 MB

**Format:**PDF, Mobi

**Read:**859

A lucid, elegant, and complete survey of set theory, this three-part treatment explores axiomatic set theory, the consistency of the continuum hypothesis, and forcing and independence results. 1996 edition.

## The Consistency Of The Axiom Of Choice And Of The Generalized Continuum Hypothesis With The Axioms Of Set Theory

**Author**: Kurt Gödel

**Editor:**

**ISBN:**

**Size**: 12,49 MB

**Format:**PDF, ePub, Docs

**Read:**206

## Set Theory And The Continuum Hypothesis

**Author**: Paul J. Cohen

**Editor:**Addison-Wesley

**ISBN:**

**Size**: 20,80 MB

**Format:**PDF, ePub

**Read:**341

## Set Theory And The Continuum Hypotheses

**Author**:

**Editor:**

**ISBN:**

**Size**: 16,83 MB

**Format:**PDF, ePub, Mobi

**Read:**383

## Set Theory

**Author**: Thomas Jech

**Editor:**Springer Science & Business Media

**ISBN:**3662224003

**Size**: 11,64 MB

**Format:**PDF, Mobi

**Read:**564

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.

## The Consistency Of The Axiom Of Choice And Of The Generalized Continuum Hypothesis Whith The Axioms Of Set Theory

**Author**: Kurt Gödel

**Editor:**

**ISBN:**

**Size**: 15,51 MB

**Format:**PDF, ePub, Docs

**Read:**856

## The Philosophy Of Set Theory

**Author**: Mary Tiles

**Editor:**Courier Corporation

**ISBN:**0486138550

**Size**: 18,61 MB

**Format:**PDF, Mobi

**Read:**939

DIVBeginning with perspectives on the finite universe and classes and Aristotelian logic, the author examines permutations, combinations, and infinite cardinalities; numbering the continuum; Cantor's transfinite paradise; axiomatic set theory, and more. /div

## Labyrinth Of Thought

**Author**: Jose Ferreiros

**Editor:**Birkhäuser

**ISBN:**3034850492

**Size**: 17,35 MB

**Format:**PDF, Docs

**Read:**477

"José Ferreirós has written a magisterial account of the history of set theory which is panoramic, balanced, and engaging. Not only does this book synthesize much previous work and provide fresh insights and points of view, but it also features a major innovation, a full-fledged treatment of the emergence of the set-theoretic approach in mathematics from the early nineteenth century. This takes up Part One of the book. Part Two analyzes the crucial developments in the last quarter of the nineteenth century, above all the work of Cantor, but also Dedekind and the interaction between the two. Lastly, Part Three details the development of set theory up to 1950, taking account of foundational questions and the emergence of the modern axiomatization." (Bulletin of Symbolic Logic)