Set Theory Of The Continuum
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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.
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.
Axiomatic Set Theory
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Author : Patrick Suppes
language : en
Publisher: Courier Corporation
Release Date : 2012-05-04
Axiomatic Set Theory written by Patrick Suppes and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-05-04 with Mathematics categories.
Geared toward upper-level undergraduates and graduate students, this treatment examines the basic paradoxes and history of set theory and advanced topics such as relations and functions, equipollence, more. 1960 edition.
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.
Cantorian Set Theory And Limitation Of Size
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Author : Michael Hallett
language : en
Publisher: Oxford University Press
Release Date : 1986
Cantorian Set Theory And Limitation Of Size written by Michael Hallett and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
This volume presents the philosophical and heuristic framework Cantor developed and explores its lasting effect on modern mathematics. "Establishes a new plateau for historical comprehension of Cantor's monumental contribution to mathematics." --The American Mathematical Monthly
The Philosophy Of Set Theory
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Author : Mary Tiles
language : en
Publisher: Courier Corporation
Release Date : 2012-03-08
The Philosophy Of Set Theory written by Mary Tiles and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-03-08 with Mathematics categories.
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
Axiomatic Set Theory
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Author : Lev D. Beklemishev
language : en
Publisher: Elsevier
Release Date : 2000-04-01
Axiomatic Set Theory written by Lev D. Beklemishev and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-01 with Computers categories.
Axiomatic Set Theory
Introduction To Set Theory Third Edition Revised And Expanded
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Author : Karel Hrbacek
language : en
Publisher: CRC Press
Release Date : 1999-06-22
Introduction To Set Theory Third Edition Revised And Expanded written by Karel Hrbacek and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-06-22 with Mathematics categories.
Thoroughly revised, updated, expanded, and reorganized to serve as a primary text for mathematics courses, Introduction to Set Theory, Third Edition covers the basics: relations, functions, orderings, finite, countable, and uncountable sets, and cardinal and ordinal numbers. It also provides five additional self-contained chapters, consolidates the material on real numbers into a single updated chapter affording flexibility in course design, supplies end-of-section problems, with hints, of varying degrees of difficulty, includes new material on normal forms and Goodstein sequences, and adds important recent ideas including filters, ultrafilters, closed unbounded and stationary sets, and partitions.
Notes On Set Theory
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Author : Yiannis Moschovakis
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Notes On Set Theory written by Yiannis Moschovakis 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 2013-04-17 with Mathematics categories.
What this book is about. The theory of sets is a vibrant, exciting math ematical theory, with its own basic notions, fundamental results and deep open problems, and with significant applications to other mathematical theories. At the same time, axiomatic set theory is often viewed as a foun dation ofmathematics: it is alleged that all mathematical objects are sets, and their properties can be derived from the relatively few and elegant axioms about sets. Nothing so simple-minded can be quite true, but there is little doubt that in standard, current mathematical practice, "making a notion precise" is essentially synonymous with "defining it in set theory. " Set theory is the official language of mathematics, just as mathematics is the official language of science. Like most authors of elementary, introductory books about sets, I have tried to do justice to both aspects of the subject. From straight set theory, these Notes cover the basic facts about "ab stract sets," including the Axiom of Choice, transfinite recursion, and car dinal and ordinal numbers. Somewhat less common is the inclusion of a chapter on "pointsets" which focuses on results of interest to analysts and introduces the reader to the Continuum Problem, central to set theory from the very beginning.
Introducing Philosophy Of Mathematics
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Author : Michele Friend
language : en
Publisher: Routledge
Release Date : 2014-12-05
Introducing Philosophy Of Mathematics written by Michele Friend and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-05 with Philosophy categories.
What is mathematics about? Does the subject-matter of mathematics exist independently of the mind or are they mental constructions? How do we know mathematics? Is mathematical knowledge logical knowledge? And how is mathematics applied to the material world? In this introduction to the philosophy of mathematics, Michele Friend examines these and other ontological and epistemological problems raised by the content and practice of mathematics. Aimed at a readership with limited proficiency in mathematics but with some experience of formal logic it seeks to strike a balance between conceptual accessibility and correct representation of the issues. Friend examines the standard theories of mathematics - Platonism, realism, logicism, formalism, constructivism and structuralism - as well as some less standard theories such as psychologism, fictionalism and Meinongian philosophy of mathematics. In each case Friend explains what characterises the position and where the divisions between them lie, including some of the arguments in favour and against each. This book also explores particular questions that occupy present-day philosophers and mathematicians such as the problem of infinity, mathematical intuition and the relationship, if any, between the philosophy of mathematics and the practice of mathematics. Taking in the canonical ideas of Aristotle, Kant, Frege and Whitehead and Russell as well as the challenging and innovative work of recent philosophers like Benacerraf, Hellman, Maddy and Shapiro, Friend provides a balanced and accessible introduction suitable for upper-level undergraduate courses and the non-specialist.