Zermelo's Axiom of Choice

Its Origins, Development, and Influence

Author: Gregory H. Moore

Publisher: Courier Corporation

ISBN: 0486488411

Category: Mathematics

Page: 410

View: 6762

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"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"--

Set Theory and the Continuum Hypothesis

Author: Paul J. Cohen,Martin Davis

Publisher: Courier Corporation

ISBN: 0486469212

Category: Mathematics

Page: 154

View: 2170

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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.

Labyrinth of Thought

A History of Set Theory and Its Role in Modern Mathematics

Author: Jose Ferreiros

Publisher: Springer Science & Business Media

ISBN: 9783764357498

Category: Mathematics

Page: 440

View: 6004

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"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)

Perspectives on the History of Mathematical Logic

Author: Thomas Drucker

Publisher: Springer Science & Business Media

ISBN: 0817647686

Category: Mathematics

Page: 195

View: 6558

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This volume offers insights into the development of mathematical logic over the last century. Arising from a special session of the history of logic at an American Mathematical Society meeting, the chapters explore technical innovations, the philosophical consequences of work during the period, and the historical and social context in which the logicians worked. The discussions herein will appeal to mathematical logicians and historians of mathematics, as well as philosophers and historians of science.

Euclid—The Creation of Mathematics

Author: Benno Artmann

Publisher: Springer Science & Business Media

ISBN: 1461214122

Category: Mathematics

Page: 349

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Euclid presents the essential of mathematics in a manner which has set a high standard for more than 2000 years. This book, an explanation of the nature of mathematics from its most important early source, is for all lovers of mathematics with a solid background in high school geometry, whether they be students or university professors.

Axiom of Choice

Author: Horst Herrlich

Publisher: Springer

ISBN: 3540342680

Category: Mathematics

Page: 198

View: 4677

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AC, the axiom of choice, because of its non-constructive character, is the most controversial mathematical axiom. It is shunned by some, used indiscriminately by others. This treatise shows paradigmatically that disasters happen without AC and they happen with AC. Illuminating examples are drawn from diverse areas of mathematics, particularly from general topology, but also from algebra, order theory, elementary analysis, measure theory, game theory, and graph theory.

Undecidable Theories

Author: Alfred Tarski,Andrzej Mostowski,Raphael Mitchel Robinson

Publisher: Elsevier

ISBN: 0444533788

Category: Decidability (Mathematical logic)

Page: 98

View: 6817

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Mathematics in Philosophy

Selected Essays

Author: Charles Parsons

Publisher: Cornell University Press

ISBN: 9780801489815

Category: Mathematics

Page: 365

View: 875

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This important book by a major American philosopher brings together eleven essays treating problems in logic and the philosophy of mathematics. A common point of view, that mathematical thought is central to our thought in general, underlies the essays. In his introduction, Parsons articulates that point of view and relates it to past and recent discussions of the foundations of mathematics.Mathematics in Philosophy is divided into three parts. Ontology—the question of the nature and extent of existence assumptions in mathematics—is the subject of Part One and recurs elsewhere. Part Two consists of essays on two important historical figures, Kant and Frege, and one contemporary, W. V. Quine. Part Three contains essays on the three interrelated notions of set, class, and truth.

Encyclopaedia of Mathematics, Supplement III

Author: Michiel Hazewinkel

Publisher: Springer Science & Business Media

ISBN: 9781402001987

Category: Mathematics

Page: 557

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This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.

Vita Mathematica

Historical Research and Integration with Teaching

Author: Ronald Calinger

Publisher: Cambridge University Press

ISBN: 9780883850978

Category: Mathematics

Page: 359

View: 4547

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Enables teachers to learn the history of mathematics and then incorporate it in undergraduate teaching.

Discovering Modern Set Theory: The basics

Author: Winfried Just,Martin Weese

Publisher: American Mathematical Soc.

ISBN: 0821802666

Category: Mathematics

Page: 210

View: 1120

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This book is an introduction to set theory for beginning graduate students who want to get a sound grounding in those aspects of set theory used extensively throughout other areas of mathematics. Topics covered include formal languages and models, the power and limitation of the Axiomatic Method, the Axiom of Choice, including the fascinating Banach-Tarski Paradox, applications of Zorn's Lemma, ordinal arithmetic, including transfinite induction, and cardinal arithmetic. The style of writing, more a dialogue with the reader than that of the Master indoctrinating the pupil, makes this also very suitable for self-study.

MAA Notes

Author: Ronald Calinger

Publisher: The Mathematical Association of America

ISBN: N.A

Category: Education

Page: N.A

View: 3715

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Handbook of Cognitive Science

An Embodied Approach

Author: Paco Calvo,Toni Gomila

Publisher: Elsevier

ISBN: 9780080914879

Category: Computers

Page: 498

View: 2653

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The Handbook of Cognitive Science provides an overview of recent developments in cognition research, relying upon non-classical approaches. Cognition is explained as the continuous interplay between brain, body, and environment, without relying on classical notions of computations and representation to explain cognition. The handbook serves as a valuable companion for readers interested in foundational aspects of cognitive science, and neuroscience and the philosophy of mind. The handbook begins with an introduction to embodied cognitive science, and then breaks up the chapters into separate sections on conceptual issues, formal approaches, embodiment in perception and action, embodiment from an artificial perspective, embodied meaning, and emotion and consciousness. Contributors to the book represent research overviews from around the globe including the US, UK, Spain, Germany, Switzerland, France, Sweden, and the Netherlands.

From Kant to Hilbert

a source book in the foundations of mathematics

Author: William Bragg Ewald

Publisher: Oxford University Press, USA

ISBN: N.A

Category: Language Arts & Disciplines

Page: 1340

View: 8633

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Dimension Theory (PMS-4)

Author: Witold Hurewicz,Henry Wallman

Publisher: Princeton University Press

ISBN: 1400875668

Category: Mathematics

Page: 174

View: 5129

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Book 4 in the Princeton Mathematical Series. Originally published in 1941. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Set theory

Author: Charles C. Pinter

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: 216

View: 553

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The History of Mathematics

Brief Version

Author: Victor J. Katz

Publisher: Addison-Wesley

ISBN: N.A

Category: Mathematics

Page: 560

View: 5933

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One of the leading historians in the mathematics field, Victor Katz provides a world view of mathematics, balancing ancient, early modern, and modern history. Egypt and Mesopotamia, Greek Mathematics to the Time of Euclid, Greek Mathematics from Archimedes to Ptolemy, Diophantus to Hypatia, Ancient and Medieval China, Ancient and Medieval India, The Mathematics of Islam, Mathematics in Medieval Europe, Mathematics in the Renaissance, Precalculus in the Seventeenth Century, Calculus in the Seventeenth Century, Analysis in the Eighteenth Century, Probability and Statistics in the Eighteenth Century, Algebra and Number Theory in the Eighteenth Century, Geometry in the Eighteenth Century, Algebra and Number Theory in the Nineteenth Century, Analysis in the Nineteenth Century, Statistics in the Nineteenth Century, Geometry in the Nineteenth Century, Aspects of the Twentieth Century For all readers interested in the history of mathematics.

Set Theory

Techniques and Applications Curaçao 1995 and Barcelona 1996 Conferences

Author: Carlos A. di Prisco,Jean A. Larson,Joan Bagaria,A.R.D. Mathias

Publisher: Springer Science & Business Media

ISBN: 9401589887

Category: Mathematics

Page: 226

View: 2393

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During the past 25 years, set theory has developed in several interesting directions. The most outstanding results cover the application of sophisticated techniques to problems in analysis, topology, infinitary combinatorics and other areas of mathematics. This book contains a selection of contributions, some of which are expository in nature, embracing various aspects of the latest developments. Amongst topics treated are forcing axioms and their applications, combinatorial principles used to construct models, and a variety of other set theoretical tools including inner models, partitions and trees. Audience: This book will be of interest to graduate students and researchers in foundational problems of mathematics.

The Foundations of Mathematics

Author: Kenneth Kunen

Publisher: N.A

ISBN: 9781904987147

Category: Mathematics

Page: 251

View: 5280

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Mathematical logic grew out of philosophical questions regarding the foundations of mathematics, but logic has now outgrown its philosophical roots, and has become an integral part of mathematics in general. This book is designed for students who plan to specialize in logic, as well as for those who are interested in the applications of logic to other areas of mathematics. Used as a text, it could form the basis of a beginning graduate-level course. There are three main chapters: Set Theory, Model Theory, and Recursion Theory. The Set Theory chapter describes the set-theoretic foundations of all of mathematics, based on the ZFC axioms. It also covers technical results about the Axiom of Choice, well-orderings, and the theory of uncountable cardinals. The Model Theory chapter discusses predicate logic and formal proofs, and covers the Completeness, Compactness, and Lowenheim-Skolem Theorems, elementary submodels, model completeness, and applications to algebra. This chapter also continues the foundational issues begun in the set theory chapter. Mathematics can now be viewed as formal proofs from ZFC. Also, model theory leads to models of set theory. This includes a discussion of absoluteness, and an analysis of models such as H( ) and R( ). The Recursion Theory chapter develops some basic facts about computable functions, and uses them to prove a number of results of foundational importance; in particular, Church's theorem on the undecidability of logical consequence, the incompleteness theorems of Godel, and Tarski's theorem on the non-definability of truth.