Zermelo S Axiom Of Choice

Author : G.H. Moore
Publisher : Springer Science & Business Media
Page : 425 pages
File Size : 45,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461394785

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Zermelo’s Axiom of Choice by G.H. Moore Pdf

This book grew out of my interest in what is common to three disciplines: mathematics, philosophy, and history. The origins of Zermelo's Axiom of Choice, as well as the controversy that it engendered, certainly lie in that intersection. Since the time of Aristotle, mathematics has been concerned alternately with its assumptions and with the objects, such as number and space, about which those assumptions were made. In the historical context of Zermelo's Axiom, I have explored both the vagaries and the fertility of this alternating concern. Though Zermelo's research has provided the focus for this book, much of it is devoted to the problems from which his work originated and to the later developments which, directly or indirectly, he inspired. A few remarks about format are in order. In this book a publication is indicated by a date after a name; so Hilbert 1926, 178 refers to page 178 of an article written by Hilbert, published in 1926, and listed in the bibliography.

Author : Gregory H. Moore
Publisher : Courier Corporation
Page : 450 pages
File Size : 46,9 Mb
Release : 2012-09-20
Category : Mathematics
ISBN : 9780486488417

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Zermelo's Axiom of Choice by Gregory H. Moore Pdf

"This book chronicles the work of mathematician Ernst Zermelo (1871-1953) and his development of set theory's crucial principle, the axiom of choice. It covers the axiom's formulation during the early 20th century, the controversy it engendered, and its current central place in set theory and mathematical logic. 1982 edition"--

Author : Thomas J. Jech
Publisher : Courier Corporation
Page : 226 pages
File Size : 55,8 Mb
Release : 2008-01-01
Category : Mathematics
ISBN : 9780486466248

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The Axiom of Choice by Thomas J. Jech Pdf

Comprehensive and self-contained text examines the axiom's relative strengths and consequences, including its consistency and independence, relation to permutation models, and examples and counterexamples of its use. 1973 edition.

Author : Lorenz Halbeisen,Regula Krapf
Publisher : Springer Nature
Page : 236 pages
File Size : 52,6 Mb
Release : 2020-10-16
Category : Mathematics
ISBN : 9783030522797

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Gödel's Theorems and Zermelo's Axioms by Lorenz Halbeisen,Regula Krapf Pdf

This book provides a concise and self-contained introduction to the foundations of mathematics. The first part covers the fundamental notions of mathematical logic, including logical axioms, formal proofs and the basics of model theory. Building on this, in the second and third part of the book the authors present detailed proofs of Gödel’s classical completeness and incompleteness theorems. In particular, the book includes a full proof of Gödel’s second incompleteness theorem which states that it is impossible to prove the consistency of arithmetic within its axioms. The final part is dedicated to an introduction into modern axiomatic set theory based on the Zermelo’s axioms, containing a presentation of Gödel’s constructible universe of sets. A recurring theme in the whole book consists of standard and non-standard models of several theories, such as Peano arithmetic, Presburger arithmetic and the real numbers. The book addresses undergraduate mathematics students and is suitable for a one or two semester introductory course into logic and set theory. Each chapter concludes with a list of exercises.

Author : John Lane Bell
Publisher : Studies in Logic. Mathematical
Page : 248 pages
File Size : 46,8 Mb
Release : 2009
Category : Mathematics
ISBN : 1904987540

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The Axiom of Choice by John Lane Bell Pdf

This book presents an overview of the development of the Axiom of Choice since its introduction by Zermelo at the beginning of the last century. The book surveys the Axiom of Choice from three perspectives. The first, or mathematical perspective, is that of the "working mathematician". This perspective brings into view the manifold applications of the Axiom of Choice-usually in the guise of Zorn s Lemma- in a great variety of areas of mathematics. The second, foundational, perspective is that of the logician or constructive mathematician concerned with the foundational status of the Axiom of Choice. The third, topos-theoretical, perspective is that taken by the mathematician or logician investigating the role of the Axiom of Choice in topos theory. Certain topics-for instance mathematical applications of the Axiom, and its relationship with logic-are discussed in considerable detail. Others-notably the consistency and independence of the Axiom of the usual systems of set theory-are given no more than summary treatment, the justification here being that these topics have been given full expositions elsewhere. It is hoped that the book will be of interest to logicians and mathematicians, both professional and prospective.

Author : Herman Rubin,Jean E. Rubin
Publisher : Elsevier
Page : 159 pages
File Size : 52,5 Mb
Release : 1963
Category : Axiom of choice
ISBN : 9780444533999

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Equivalents of the Axiom of Choice by Herman Rubin,Jean E. Rubin Pdf

Author : Alfred North Whitehead,Bertrand Russell
Publisher : Cambridge University Press
Page : 524 pages
File Size : 42,7 Mb
Release : 1927
Category : Mathematics
ISBN : 052106791X

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Principia Mathematica by Alfred North Whitehead,Bertrand Russell Pdf

The Principia Mathematica has long been recognised as one of the intellectual landmarks of the century.

Author : Sean Morris
Publisher : Cambridge University Press
Page : 221 pages
File Size : 55,6 Mb
Release : 2018-12-13
Category : History
ISBN : 9781107152502

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Quine, New Foundations, and the Philosophy of Set Theory by Sean Morris Pdf

Provides an accessible mathematical and philosophical account of Quine's set theory, New Foundations.

Author : G. H. Moore
Publisher : Unknown
Page : 428 pages
File Size : 40,8 Mb
Release : 1982-11-17
Category : Electronic
ISBN : 1461394791

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Zermelo's Axiom of Choice by G. H. Moore Pdf

Author : Paul J. Cohen
Publisher : Courier Corporation
Page : 196 pages
File Size : 55,5 Mb
Release : 2008-12-09
Category : Mathematics
ISBN : 9780486469218

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Set Theory and the Continuum Hypothesis by Paul J. Cohen Pdf

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.

Author : Régine Douady,Adrien Douady
Publisher : Springer Nature
Page : 462 pages
File Size : 42,8 Mb
Release : 2020-07-13
Category : Mathematics
ISBN : 9783030327965

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Algebra and Galois Theories by Régine Douady,Adrien Douady Pdf

Galois theory has such close analogies with the theory of coverings that algebraists use a geometric language to speak of field extensions, while topologists speak of "Galois coverings". This book endeavors to develop these theories in a parallel way, starting with that of coverings, which better allows the reader to make images. The authors chose a plan that emphasizes this parallelism. The intention is to allow to transfer to the algebraic framework of Galois theory the geometric intuition that one can have in the context of coverings. This book is aimed at graduate students and mathematicians curious about a non-exclusively algebraic view of Galois theory.

Author : Michael Potter
Publisher : Clarendon Press
Page : 362 pages
File Size : 52,8 Mb
Release : 2004-01-15
Category : Philosophy
ISBN : 9780191556432

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Set Theory and its Philosophy by Michael Potter Pdf

Michael Potter presents a comprehensive new philosophical introduction to set theory. Anyone wishing to work on the logical foundations of mathematics must understand set theory, which lies at its heart. Potter offers a thorough account of cardinal and ordinal arithmetic, and the various axiom candidates. He discusses in detail the project of set-theoretic reduction, which aims to interpret the rest of mathematics in terms of set theory. The key question here is how to deal with the paradoxes that bedevil set theory. Potter offers a strikingly simple version of the most widely accepted response to the paradoxes, which classifies sets by means of a hierarchy of levels. What makes the book unique is that it interweaves a careful presentation of the technical material with a penetrating philosophical critique. Potter does not merely expound the theory dogmatically but at every stage discusses in detail the reasons that can be offered for believing it to be true. Set Theory and its Philosophy is a key text for philosophy, mathematical logic, and computer science.

Author : Eric Schechter
Publisher : Academic Press
Page : 907 pages
File Size : 48,5 Mb
Release : 1996-10-24
Category : Mathematics
ISBN : 9780080532998

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Handbook of Analysis and Its Foundations by Eric Schechter Pdf

Handbook of Analysis and Its Foundations is a self-contained and unified handbook on mathematical analysis and its foundations. Intended as a self-study guide for advanced undergraduates and beginning graduatestudents in mathematics and a reference for more advanced mathematicians, this highly readable book provides broader coverage than competing texts in the area. Handbook of Analysis and Its Foundations provides an introduction to a wide range of topics, including: algebra; topology; normed spaces; integration theory; topological vector spaces; and differential equations. The author effectively demonstrates the relationships between these topics and includes a few chapters on set theory and logic to explain the lack of examples for classical pathological objects whose existence proofs are not constructive. More complete than any other book on the subject, students will find this to be an invaluable handbook. Covers some hard-to-find results including: Bessagas and Meyers converses of the Contraction Fixed Point Theorem Redefinition of subnets by Aarnes and Andenaes Ghermans characterization of topological convergences Neumanns nonlinear Closed Graph Theorem van Maarens geometry-free version of Sperners Lemma Includes a few advanced topics in functional analysis Features all areas of the foundations of analysis except geometry Combines material usually found in many different sources, making this unified treatment more convenient for the user Has its own webpage: http://math.vanderbilt.edu/

Author : Stephen George Simpson
Publisher : Cambridge University Press
Page : 461 pages
File Size : 52,6 Mb
Release : 2009-05-29
Category : Mathematics
ISBN : 9780521884396

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Subsystems of Second Order Arithmetic by Stephen George Simpson Pdf

This volume examines appropriate axioms for mathematics to prove particular theorems in core areas.

Author : Nikolai Konstantinovich Vereshchagin,Alexander Shen
Publisher : American Mathematical Soc.
Page : 130 pages
File Size : 48,8 Mb
Release : 2002
Category : Set theory
ISBN : 9780821827314

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Basic Set Theory by Nikolai Konstantinovich Vereshchagin,Alexander Shen Pdf

The main notions of set theory (cardinals, ordinals, transfinite induction) are fundamental to all mathematicians, not only to those who specialize in mathematical logic or set-theoretic topology. Basic set theory is generally given a brief overview in courses on analysis, algebra, or topology, even though it is sufficiently important, interesting, and simple to merit its own leisurely treatment. This book provides just that: a leisurely exposition for a diversified audience. It is suitable for a broad range of readers, from undergraduate students to professional mathematicians who want to finally find out what transfinite induction is and why it is always replaced by Zorn's Lemma. The text introduces all main subjects of ``naive'' (nonaxiomatic) set theory: functions, cardinalities, ordered and well-ordered sets, transfinite induction and its applications, ordinals, and operations on ordinals. Included are discussions and proofs of the Cantor-Bernstein Theorem, Cantor's diagonal method, Zorn's Lemma, Zermelo's Theorem, and Hamel bases. With over 150 problems, the book is a complete and accessible introduction to the subject.