Set Theory And Foundations Of Mathematics

Author : Douglas Cenzer,Jean Larson,Christopher Porter,Jindrich Zapletal
Publisher : World Scientific
Page : 222 pages
File Size : 47,5 Mb
Release : 2020-04-04
Category : Mathematics
ISBN : 9789811201943

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Set Theory And Foundations Of Mathematics: An Introduction To Mathematical Logic - Volume I: Set Theory by Douglas Cenzer,Jean Larson,Christopher Porter,Jindrich Zapletal Pdf

This book provides an introduction to axiomatic set theory and descriptive set theory. It is written for the upper level undergraduate or beginning graduate students to help them prepare for advanced study in set theory and mathematical logic as well as other areas of mathematics, such as analysis, topology, and algebra.The book is designed as a flexible and accessible text for a one-semester introductory course in set theory, where the existing alternatives may be more demanding or specialized. Readers will learn the universally accepted basis of the field, with several popular topics added as an option. Pointers to more advanced study are scattered throughout the text.

Author : Luca Incurvati
Publisher : Cambridge University Press
Page : 255 pages
File Size : 50,6 Mb
Release : 2020-01-23
Category : History
ISBN : 9781108497824

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Conceptions of Set and the Foundations of Mathematics by Luca Incurvati Pdf

Presents a detailed and critical examination of the available conceptions of set and proposes a novel version.

Author : John P. Mayberry
Publisher : Cambridge University Press
Page : 454 pages
File Size : 49,5 Mb
Release : 2000
Category : Mathematics
ISBN : 0521770343

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The Foundations of Mathematics in the Theory of Sets by John P. Mayberry Pdf

This 2001 book will appeal to mathematicians and philosophers interested in the foundations of mathematics.

Author : Abraham Adolf Fraenkel
Publisher : Unknown
Page : 297 pages
File Size : 51,8 Mb
Release : 1968
Category : Electronic
ISBN : OCLC:803151895

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Abstract Set Theory by Abraham Adolf Fraenkel Pdf

Author : Stefania Centrone,Deborah Kant,Deniz Sarikaya
Publisher : Springer Nature
Page : 511 pages
File Size : 40,9 Mb
Release : 2019-11-11
Category : Mathematics
ISBN : 9783030156558

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Reflections on the Foundations of Mathematics by Stefania Centrone,Deborah Kant,Deniz Sarikaya Pdf

This edited work presents contemporary mathematical practice in the foundational mathematical theories, in particular set theory and the univalent foundations. It shares the work of significant scholars across the disciplines of mathematics, philosophy and computer science. Readers will discover systematic thought on criteria for a suitable foundation in mathematics and philosophical reflections around the mathematical perspectives. The volume is divided into three sections, the first two of which focus on the two most prominent candidate theories for a foundation of mathematics. Readers may trace current research in set theory, which has widely been assumed to serve as a framework for foundational issues, as well as new material elaborating on the univalent foundations, considering an approach based on homotopy type theory (HoTT). The third section then builds on this and is centred on philosophical questions connected to the foundations of mathematics. Here, the authors contribute to discussions on foundational criteria with more general thoughts on the foundations of mathematics which are not connected to particular theories. This book shares the work of some of the most important scholars in the fields of set theory (S. Friedman), non-classical logic (G. Priest) and the philosophy of mathematics (P. Maddy). The reader will become aware of the advantages of each theory and objections to it as a foundation, following the latest and best work across the disciplines and it is therefore a valuable read for anyone working on the foundations of mathematics or in the philosophy of mathematics.

Author : A.A. Fraenkel,Y. Bar-Hillel,A. Levy
Publisher : Elsevier
Page : 415 pages
File Size : 50,9 Mb
Release : 1973-12-01
Category : Computers
ISBN : 9780080887050

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Foundations of Set Theory by A.A. Fraenkel,Y. Bar-Hillel,A. Levy Pdf

Foundations of Set Theory discusses the reconstruction undergone by set theory in the hands of Brouwer, Russell, and Zermelo. Only in the axiomatic foundations, however, have there been such extensive, almost revolutionary, developments. This book tries to avoid a detailed discussion of those topics which would have required heavy technical machinery, while describing the major results obtained in their treatment if these results could be stated in relatively non-technical terms. This book comprises five chapters and begins with a discussion of the antinomies that led to the reconstruction of set theory as it was known before. It then moves to the axiomatic foundations of set theory, including a discussion of the basic notions of equality and extensionality and axioms of comprehension and infinity. The next chapters discuss type-theoretical approaches, including the ideal calculus, the theory of types, and Quine's mathematical logic and new foundations; intuitionistic conceptions of mathematics and its constructive character; and metamathematical and semantical approaches, such as the Hilbert program. This book will be of interest to mathematicians, logicians, and statisticians.

Author : Norman T. Hamilton,Joseph Landin
Publisher : Courier Dover Publications
Page : 288 pages
File Size : 46,7 Mb
Release : 2018-05-16
Category : Mathematics
ISBN : 9780486830476

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Set Theory: The Structure of Arithmetic by Norman T. Hamilton,Joseph Landin Pdf

This text is formulated on the fundamental idea that much of mathematics, including the classical number systems, can best be based on set theory. 1961 edition.

Author : F. William Lawvere,Robert Rosebrugh
Publisher : Cambridge University Press
Page : 280 pages
File Size : 45,8 Mb
Release : 2003-01-27
Category : Mathematics
ISBN : 0521010608

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Sets for Mathematics by F. William Lawvere,Robert Rosebrugh Pdf

In this book, first published in 2003, categorical algebra is used to build a foundation for the study of geometry, analysis, and algebra.

Author : Juliette Kennedy,Roman Kossak
Publisher : Cambridge University Press
Page : 242 pages
File Size : 49,9 Mb
Release : 2011-09-01
Category : Mathematics
ISBN : 1107008042

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Set Theory, Arithmetic, and Foundations of Mathematics by Juliette Kennedy,Roman Kossak Pdf

This collection of papers from various areas of mathematical logic showcases the remarkable breadth and richness of the field. Leading authors reveal how contemporary technical results touch upon foundational questions about the nature of mathematics. Highlights of the volume include: a history of Tennenbaum's theorem in arithmetic; a number of papers on Tennenbaum phenomena in weak arithmetics as well as on other aspects of arithmetics, such as interpretability; the transcript of Gödel's previously unpublished 1972-1975 conversations with Sue Toledo, along with an appreciation of the same by Curtis Franks; Hugh Woodin's paper arguing against the generic multiverse view; Anne Troelstra's history of intuitionism through 1991; and Aki Kanamori's history of the Suslin problem in set theory. The book provides a historical and philosophical treatment of particular theorems in arithmetic and set theory, and is ideal for researchers and graduate students in mathematical logic and philosophy of mathematics.

Author : Robert Lee Moore
Publisher : American Mathematical Soc.
Page : 434 pages
File Size : 45,9 Mb
Release : 1932-12-31
Category : Mathematics
ISBN : 9780821810132

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Foundations of Point Set Theory by Robert Lee Moore Pdf

Author : Herbert B. Enderton
Publisher : Academic Press
Page : 279 pages
File Size : 45,6 Mb
Release : 1977-05-23
Category : Mathematics
ISBN : 9780080570426

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Elements of Set Theory by Herbert B. Enderton Pdf

This is an introductory undergraduate textbook in set theory. In mathematics these days, essentially everything is a set. Some knowledge of set theory is necessary part of the background everyone needs for further study of mathematics. It is also possible to study set theory for its own interest--it is a subject with intruiging results anout simple objects. This book starts with material that nobody can do without. There is no end to what can be learned of set theory, but here is a beginning.

Author : Jose Ferreiros
Publisher : Springer Science & Business Media
Page : 472 pages
File Size : 52,8 Mb
Release : 2001-11-01
Category : Mathematics
ISBN : 3764357495

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Labyrinth of Thought by Jose Ferreiros Pdf

"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)

Author : Robert R. Stoll
Publisher : Courier Corporation
Page : 512 pages
File Size : 51,9 Mb
Release : 2012-05-23
Category : Mathematics
ISBN : 9780486139647

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Set Theory and Logic by Robert R. Stoll Pdf

Explores sets and relations, the natural number sequence and its generalization, extension of natural numbers to real numbers, logic, informal axiomatic mathematics, Boolean algebras, informal axiomatic set theory, several algebraic theories, and 1st-order theories.

Author : Douglas Cenzer,Jean Larson,Christopher Porter,Jindrich Zapletal
Publisher : World Scientific Publishing Company
Page : 200 pages
File Size : 50,5 Mb
Release : 2020
Category : Mathematics
ISBN : 9811243840

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Set Theory and Foundations of Mathematics by Douglas Cenzer,Jean Larson,Christopher Porter,Jindrich Zapletal Pdf

"This book provides an introduction to axiomatic set theory and descriptive set theory. It is written for the upper level undergraduate or beginning graduate students to help them prepare for advanced study in set theory and mathematical logic as well as other areas of mathematics, such as analysis, topology, and algebra. The book is designed as a flexible and accessible text for a one-semester introductory course in set theory, where the existing alternatives may be more demanding or specialized. Readers will learn the universally accepted basis of the field, with several popular topics added as an option. Pointers to more advanced study are scattered throughout the text"--

Author : Azriel Levy
Publisher : Courier Corporation
Page : 418 pages
File Size : 52,7 Mb
Release : 2012-06-11
Category : Mathematics
ISBN : 9780486150734

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Basic Set Theory by Azriel Levy Pdf

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.