Set Theory And The Continuum Hypothesis

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Set Theory And The Continuum Hypothesis

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Author : Paul J. Cohen
language : en
Publisher: Courier Corporation
Release Date : 2008-12-09

Set Theory And The Continuum Hypothesis written by Paul J. Cohen and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-09 with Mathematics categories.

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.

Set Theory And The Continuum Hypothesis

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Author : Paul J. Cohen
language : en
Publisher: Courier Corporation
Release Date : 2012-08-15

Set Theory And The Continuum Hypothesis written by Paul J. Cohen and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-15 with Mathematics categories.

This exploration of a notorious mathematical problem is the work of the man who discovered the solution. The award-winning author employs intuitive explanations and detailed proofs in this self-contained treatment. 1966 edition. Copyright renewed 1994.

Set Theory And The Continuum Problem

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Author : Raymond M. Smullyan
language : en
Publisher: Oxford University Press, USA
Release Date : 1996

Set Theory And The Continuum Problem written by Raymond M. Smullyan and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.

Set Theory and the Continuum Problem is a novel introduction to set theory, including axiomatic development, consistency, and independence results. It is self-contained and covers all the set theory that a mathematician should know. Part I introduces set theory, including basic axioms, development of the natural number system, Zorn's Lemma and other maximal principles. Part II proves the consistency of the continuum hypothesis and the axiom of choice, with material on collapsing mappings, model-theoretic results, and constructible sets. Part III presents a version of Cohen's proofs of the independence of the continuum hypothesis and the axiom of choice. It also presents, for the first time in a textbook, the double induction and superinduction principles, and Cowen's theorem. The book will interest students and researchers in logic and set theory.

Set Theory And Continuum Hypothesis

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Author : Paul J. Cohen
language : en
Publisher:
Release Date : 1969

Set Theory And Continuum Hypothesis written by Paul J. Cohen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Set theory categories.

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

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Author : Kurt Gödel
language : en
Publisher: Princeton University Press
Release Date : 1940

The Consistency Of The Axiom Of Choice And Of The Generalized Continuum Hypothesis With The Axioms Of Set Theory written by Kurt Gödel and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1940 with Logic, Symbolic and mathematical categories.

Set Theory Of The Continuum

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Author : Haim Judah
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Set Theory Of The Continuum written by Haim Judah and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Primarily consisting of talks presented at a workshop at the MSRI during its "Logic Year" 1989-90, this volume is intended to reflect the whole spectrum of activities in set theory. The first section of the book comprises the invited papers surveying the state of the art in a wide range of topics of set-theoretic research. The second section includes research papers on various aspects of set theory and its relation to algebra and topology. Contributors include: J.Bagaria, T. Bartoszynski, H. Becker, P. Dehornoy, Q. Feng, M. Foreman, M. Gitik, L. Harrington, S. Jackson, H. Judah, W. Just, A.S. Kechris, A. Louveau, S. MacLane, M. Magidor, A.R.D. Mathias, G. Melles, W.J. Mitchell, S. Shelah, R.A. Shore, R.I. Soare, L.J. Stanley, B. Velikovic, H. Woodin.

An Introduction To Homological Algebra

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Author : Charles A. Weibel
language : en
Publisher: Cambridge University Press
Release Date : 1995-10-27

An Introduction To Homological Algebra written by Charles A. Weibel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-10-27 with Mathematics categories.

The landscape of homological algebra has evolved over the last half-century into a fundamental tool for the working mathematician. This book provides a unified account of homological algebra as it exists today. The historical connection with topology, regular local rings, and semi-simple Lie algebras are also described. This book is suitable for second or third year graduate students. The first half of the book takes as its subject the canonical topics in homological algebra: derived functors, Tor and Ext, projective dimensions and spectral sequences. Homology of group and Lie algebras illustrate these topics. Intermingled are less canonical topics, such as the derived inverse limit functor lim1, local cohomology, Galois cohomology, and affine Lie algebras. The last part of the book covers less traditional topics that are a vital part of the modern homological toolkit: simplicial methods, Hochschild and cyclic homology, derived categories and total derived functors. By making these tools more accessible, the book helps to break down the technological barrier between experts and casual users of homological algebra.

Combinatorial Set Theory

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Author : Lorenz J. Halbeisen
language : en
Publisher: Springer
Release Date : 2017-12-20

Combinatorial Set Theory written by Lorenz J. Halbeisen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-20 with Mathematics categories.

This book, now in a thoroughly revised second edition, provides a comprehensive and accessible introduction to modern set theory. Following an overview of basic notions in combinatorics and first-order logic, the author outlines the main topics of classical set theory in the second part, including Ramsey theory and the axiom of choice. The revised edition contains new permutation models and recent results in set theory without the axiom of choice. The third part explains the sophisticated technique of forcing in great detail, now including a separate chapter on Suslin’s problem. The technique is used to show that certain statements are neither provable nor disprovable from the axioms of set theory. In the final part, some topics of classical set theory are revisited and further developed in light of forcing, with new chapters on Sacks Forcing and Shelah’s astonishing construction of a model with finitely many Ramsey ultrafilters. Written for graduate students in axiomatic set theory, Combinatorial Set Theory will appeal to all researchers interested in the foundations of mathematics. With extensive reference lists and historical remarks at the end of each chapter, this book is suitable for self-study.

Labyrinth Of Thought

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Author : Jose Ferreiros
language : en
Publisher: Springer Science & Business Media
Release Date : 2001-11-01

Labyrinth Of Thought written by Jose Ferreiros and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-11-01 with Mathematics categories.

"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)

Basic Set Theory

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Author : Azriel Levy
language : en
Publisher: Courier Corporation
Release Date : 2012-06-11

Basic Set Theory written by Azriel Levy and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-11 with Mathematics categories.

Although this book deals with basic set theory (in general, it stops short of areas where model-theoretic methods are used) on a rather advanced level, it does it at an unhurried pace. This enables the author to pay close attention to interesting and important aspects of the topic that might otherwise be skipped over. Written for upper-level undergraduate and graduate students, the book is divided into two parts. The first covers pure set theory, including the basic notions, order and well-foundedness, cardinal numbers, the ordinals, and the axiom of choice and some of its consequences. The second part deals with applications and advanced topics, among them a review of point set topology, the real spaces, Boolean algebras, and infinite combinatorics and large cardinals. A helpful appendix deals with eliminability and conservation theorems, while numerous exercises supply additional information on the subject matter and help students test their grasp of the material. 1979 edition. 20 figures.