Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume I Set Theory

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Set Theory And Foundations Of Mathematics: An Introduction To Mathematical Logic - Volume I: Set Theory

Douglas Cenzer,Jean Larson,Christopher Porter,Jindrich Zapletal
Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume I Set Theory Book PDF

Author : Douglas Cenzer,Jean Larson,Christopher Porter,Jindrich Zapletal
Publisher : World Scientific
Page : 222 pages
File Size : 41,6 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.

Set Theory And Foundations Of Mathematics: An Introduction To Mathematical Logic - Volume Ii: Foundations Of Mathematics

Douglas Cenzer,Jean Larson,Christopher Porter,Jindrich Zapletal
Set Theory And Foundations Of Mathematics An Introduction To Mathematical Logic Volume Ii Foundations Of Mathematics Book PDF

Author : Douglas Cenzer,Jean Larson,Christopher Porter,Jindrich Zapletal
Publisher : World Scientific
Page : 254 pages
File Size : 52,5 Mb
Release : 2022-01-27
Category : Mathematics
ISBN : 9789811243868

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

This book provides an introduction to mathematical logic and the foundations of mathematics. It will help prepare students for advanced study in set theory and mathematical logic as well as other areas of mathematics, such as analysis, topology, and algebra. The presentation of finite state and Turing machines leads to the Halting Problem and Gödel's Incompleteness Theorem, which have broad academic interest, particularly in computer science and philosophy.

A First Course in Mathematical Logic and Set Theory

Michael L. O'Leary
A First Course in Mathematical Logic and Set Theory Book PDF

Author : Michael L. O'Leary
Publisher : John Wiley & Sons
Page : 464 pages
File Size : 45,8 Mb
Release : 2015-09-08
Category : Mathematics
ISBN : 9780470905883

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A First Course in Mathematical Logic and Set Theory by Michael L. O'Leary Pdf

A mathematical introduction to the theory and applications of logic and set theory with an emphasis on writing proofs Highlighting the applications and notations of basic mathematical concepts within the framework of logic and set theory, A First Course in Mathematical Logic and Set Theory introduces how logic is used to prepare and structure proofs and solve more complex problems. The book begins with propositional logic, including two-column proofs and truth table applications, followed by first-order logic, which provides the structure for writing mathematical proofs. Set theory is then introduced and serves as the basis for defining relations, functions, numbers, mathematical induction, ordinals, and cardinals. The book concludes with a primer on basic model theory with applications to abstract algebra. A First Course in Mathematical Logic and Set Theory also includes: Section exercises designed to show the interactions between topics and reinforce the presented ideas and concepts Numerous examples that illustrate theorems and employ basic concepts such as Euclid’s lemma, the Fibonacci sequence, and unique factorization Coverage of important theorems including the well-ordering theorem, completeness theorem, compactness theorem, as well as the theorems of Löwenheim–Skolem, Burali-Forti, Hartogs, Cantor–Schröder–Bernstein, and König An excellent textbook for students studying the foundations of mathematics and mathematical proofs, A First Course in Mathematical Logic and Set Theory is also appropriate for readers preparing for careers in mathematics education or computer science. In addition, the book is ideal for introductory courses on mathematical logic and/or set theory and appropriate for upper-undergraduate transition courses with rigorous mathematical reasoning involving algebra, number theory, or analysis.

Set Theory and Foundations of Mathematics

Douglas Cenzer,Jean Larson,Christopher Porter,Jindrich Zapletal
Set Theory and Foundations of Mathematics Book PDF

Author : Douglas Cenzer,Jean Larson,Christopher Porter,Jindrich Zapletal
Publisher : World Scientific Publishing Company
Page : 200 pages
File Size : 54,6 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"--

Introduction to Mathematical Logic

Jerome Malitz
Introduction to Mathematical Logic Book PDF

Author : Jerome Malitz
Publisher : Springer Science & Business Media
Page : 209 pages
File Size : 53,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461394419

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Introduction to Mathematical Logic by Jerome Malitz Pdf

This book is intended as an undergraduate senior level or beginning graduate level text for mathematical logic. There are virtually no prere quisites, although a familiarity with notions encountered in a beginning course in abstract algebra such as groups, rings, and fields will be useful in providing some motivation for the topics in Part III. An attempt has been made to develop the beginning of each part slowly and then to gradually quicken the pace and the complexity of the material. Each part ends with a brief introduction to selected topics of current interest. The text is divided into three parts: one dealing with set theory, another with computable function theory, and the last with model theory. Part III relies heavily on the notation, concepts and results discussed in Part I and to some extent on Part II. Parts I and II are independent of each other, and each provides enough material for a one semester course. The exercises cover a wide range of difficulty with an emphasis on more routine problems in the earlier sections of each part in order to familiarize the reader with the new notions and methods. The more difficult exercises are accompanied by hints. In some cases significant theorems are devel oped step by step with hints in the problems. Such theorems are not used later in the sequence.

Concise Introduction to Logic and Set Theory

Iqbal H. Jebril,Hemen Dutta,Ilwoo Cho
Concise Introduction to Logic and Set Theory Book PDF

Author : Iqbal H. Jebril,Hemen Dutta,Ilwoo Cho
Publisher : CRC Press
Page : 170 pages
File Size : 52,7 Mb
Release : 2021-09-30
Category : Technology & Engineering
ISBN : 9780429665981

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Concise Introduction to Logic and Set Theory by Iqbal H. Jebril,Hemen Dutta,Ilwoo Cho Pdf

This book deals with two important branches of mathematics, namely, logic and set theory. Logic and set theory are closely related and play very crucial roles in the foundation of mathematics, and together produce several results in all of mathematics. The topics of logic and set theory are required in many areas of physical sciences, engineering, and technology. The book offers solved examples and exercises, and provides reasonable details to each topic discussed, for easy understanding. The book is designed for readers from various disciplines where mathematical logic and set theory play a crucial role. The book will be of interested to students and instructors in engineering, mathematics, computer science, and technology.

Foundations of Set Theory

A.A. Fraenkel,Y. Bar-Hillel,A. Levy
Foundations of Set Theory Book PDF

Author : A.A. Fraenkel,Y. Bar-Hillel,A. Levy
Publisher : Elsevier
Page : 415 pages
File Size : 49,8 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.

Set Theory: The Structure of Arithmetic

Norman T. Hamilton,Joseph Landin
Set Theory The Structure of Arithmetic Book PDF

Author : Norman T. Hamilton,Joseph Landin
Publisher : Courier Dover Publications
Page : 288 pages
File Size : 43,9 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.

Set Theory and Logic

Robert R. Stoll
Set Theory and Logic Book PDF

Author : Robert R. Stoll
Publisher : Courier Corporation
Page : 512 pages
File Size : 54,5 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.

Set Theory and its Philosophy

Michael Potter
Set Theory and its Philosophy Book PDF

Author : Michael Potter
Publisher : Clarendon Press
Page : 362 pages
File Size : 52,9 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.

Introduction to the Foundations of Mathematics

Raymond L. Wilder
Introduction to the Foundations of Mathematics Book PDF

Author : Raymond L. Wilder
Publisher : Courier Corporation
Page : 352 pages
File Size : 55,7 Mb
Release : 2013-09-26
Category : Mathematics
ISBN : 9780486276205

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Introduction to the Foundations of Mathematics by Raymond L. Wilder Pdf

Classic undergraduate text acquaints students with fundamental concepts and methods of mathematics. Topics include axiomatic method, set theory, infinite sets, groups, intuitionism, formal systems, mathematical logic, and much more. 1965 second edition.

Surveys in Set Theory

A. R. D. Mathias
Surveys in Set Theory Book PDF

Author : A. R. D. Mathias
Publisher : Cambridge University Press
Page : 257 pages
File Size : 49,8 Mb
Release : 1983-10-13
Category : Mathematics
ISBN : 9780521277334

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Surveys in Set Theory by A. R. D. Mathias Pdf

This book comprises five expository articles and two research papers on topics of current interest in set theory and the foundations of mathematics. Articles by Baumgartner and Devlin introduce the reader to proper forcing. This is a development by Saharon Shelah of Cohen's method which has led to solutions of problems that resisted attack by forcing methods as originally developed in the 1960s. The article by Guaspari is an introduction to descriptive set theory, a subject that has developed dramatically in the last few years. Articles by Kanamori and Stanley discuss one of the most difficult concepts in contemporary set theory, that of the morass, first created by Ronald Jensen in 1971 to solve the gap-two conjecture in model theory, assuming Gödel's axiom of constructibility. The papers by Prikry and Shelah complete the volume by giving the reader the flavour of contemporary research in set theory. This book will be of interest to graduate students and research workers in set theory and mathematical logic.

Notes on Logic and Set Theory

P. T. Johnstone
Notes on Logic and Set Theory Book PDF

Author : P. T. Johnstone
Publisher : Cambridge University Press
Page : 128 pages
File Size : 50,9 Mb
Release : 1987-10-08
Category : Mathematics
ISBN : 0521335027

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Notes on Logic and Set Theory by P. T. Johnstone Pdf

A succinct introduction to mathematical logic and set theory, which together form the foundations for the rigorous development of mathematics. Suitable for all introductory mathematics undergraduates, Notes on Logic and Set Theory covers the basic concepts of logic: first-order logic, consistency, and the completeness theorem, before introducing the reader to the fundamentals of axiomatic set theory. Successive chapters examine the recursive functions, the axiom of choice, ordinal and cardinal arithmetic, and the incompleteness theorems. Dr. Johnstone has included numerous exercises designed to illustrate the key elements of the theory and to provide applications of basic logical concepts to other areas of mathematics.

Introduction to Mathematical Logic, Fourth Edition

Elliott Mendelson
Introduction to Mathematical Logic Fourth Edition Book PDF

Author : Elliott Mendelson
Publisher : CRC Press
Page : 464 pages
File Size : 40,9 Mb
Release : 1997-06-01
Category : Mathematics
ISBN : 0412808307

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Introduction to Mathematical Logic, Fourth Edition by Elliott Mendelson Pdf

The Fourth Edition of this long-established text retains all the key features of the previous editions, covering the basic topics of a solid first course in mathematical logic. This edition includes an extensive appendix on second-order logic, a section on set theory with urlements, and a section on the logic that results when we allow models with empty domains. The text contains numerous exercises and an appendix furnishes answers to many of them. Introduction to Mathematical Logic includes: propositional logic first-order logic first-order number theory and the incompleteness and undecidability theorems of Gödel, Rosser, Church, and Tarski axiomatic set theory theory of computability The study of mathematical logic, axiomatic set theory, and computability theory provides an understanding of the fundamental assumptions and proof techniques that form basis of mathematics. Logic and computability theory have also become indispensable tools in theoretical computer science, including artificial intelligence. Introduction to Mathematical Logic covers these topics in a clear, reader-friendly style that will be valued by anyone working in computer science as well as lecturers and researchers in mathematics, philosophy, and related fields.

The Foundations of Mathematics in the Theory of Sets

John P. Mayberry
The Foundations of Mathematics in the Theory of Sets Book PDF

Author : John P. Mayberry
Publisher : Cambridge University Press
Page : 454 pages
File Size : 54,8 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.