Notes On Logic And Set Theory

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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 : 50,8 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.

Notes on Set Theory

Yiannis Moschovakis
Notes on Set Theory Book PDF

Author : Yiannis Moschovakis
Publisher : Springer Science & Business Media
Page : 280 pages
File Size : 45,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475741537

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Notes on Set Theory by Yiannis Moschovakis Pdf

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.

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 : 54,6 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, Logic and Their Limitations

Moshe Machover
Set Theory Logic and Their Limitations Book PDF

Author : Moshe Machover
Publisher : Cambridge University Press
Page : 304 pages
File Size : 55,9 Mb
Release : 1996-05-23
Category : Mathematics
ISBN : 0521479983

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Set Theory, Logic and Their Limitations by Moshe Machover Pdf

This is an introduction to set theory and logic that starts completely from scratch. The text is accompanied by many methodological remarks and explanations. A rigorous axiomatic presentation of Zermelo-Fraenkel set theory is given, demonstrating how the basic concepts of mathematics have apparently been reduced to set theory. This is followed by a presentation of propositional and first-order logic. Concepts and results of recursion theory are explained in intuitive terms, and the author proves and explains the limitative results of Skolem, Tarski, Church and Gödel (the celebrated incompleteness theorems). For students of mathematics or philosophy this book provides an excellent introduction to logic and set theory.

Lectures in Logic and Set Theory: Volume 2, Set Theory

George Tourlakis
Lectures in Logic and Set Theory Volume 2 Set Theory Book PDF

Author : George Tourlakis
Publisher : Cambridge University Press
Page : 0 pages
File Size : 49,5 Mb
Release : 2011-07-21
Category : Mathematics
ISBN : 0521168481

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Lectures in Logic and Set Theory: Volume 2, Set Theory by George Tourlakis Pdf

Volume II, on formal (ZFC) set theory, incorporates a self-contained "chapter 0" on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques provides a solid foundation in set theory and a thorough context for the presentation of advanced topics (such as absoluteness, relative consistency results, two expositions of Godel's construstive universe, numerous ways of viewing recursion and Cohen forcing).

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 : 43,7 Mb
Release : 1987-10-08
Category : Mathematics
ISBN : 0521336929

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

This short textbook provides a succinct introduction to mathematical logic and set theory, which together form the foundations for the rigorous development of mathematics. It will be suitable for all mathematics undergraduates coming to the subject for the first time. The book is based on lectures given at the University of Cambridge and 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. There are also chapters on 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. Consequently the book, while making an attractive first textbook for those who plan to specialise in logic, will be particularly valuable for mathematics and computer scientists whose primary interests lie elsewhere.

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 : 55,8 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.

Logic for Mathematicians

J. Barkley Rosser
Logic for Mathematicians Book PDF

Author : J. Barkley Rosser
Publisher : Courier Dover Publications
Page : 587 pages
File Size : 40,7 Mb
Release : 2008-12-18
Category : Mathematics
ISBN : 9780486468983

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Logic for Mathematicians by J. Barkley Rosser Pdf

Examination of essential topics and theorems assumes no background in logic. "Undoubtedly a major addition to the literature of mathematical logic." — Bulletin of the American Mathematical Society. 1978 edition.

Computational Logic and Set Theory

Jacob T. Schwartz,Domenico Cantone,Eugenio G. Omodeo
Computational Logic and Set Theory Book PDF

Author : Jacob T. Schwartz,Domenico Cantone,Eugenio G. Omodeo
Publisher : Springer Science & Business Media
Page : 426 pages
File Size : 46,7 Mb
Release : 2011-07-16
Category : Computers
ISBN : 9780857298089

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Computational Logic and Set Theory by Jacob T. Schwartz,Domenico Cantone,Eugenio G. Omodeo Pdf

This must-read text presents the pioneering work of the late Professor Jacob (Jack) T. Schwartz on computational logic and set theory and its application to proof verification techniques, culminating in the ÆtnaNova system, a prototype computer program designed to verify the correctness of mathematical proofs presented in the language of set theory. Topics and features: describes in depth how a specific first-order theory can be exploited to model and carry out reasoning in branches of computer science and mathematics; presents an unique system for automated proof verification in large-scale software systems; integrates important proof-engineering issues, reflecting the goals of large-scale verifiers; includes an appendix showing formalized proofs of ordinals, of various properties of the transitive closure operation, of finite and transfinite induction principles, and of Zorn’s lemma.

Elements of Set Theory

Herbert B. Enderton
Elements of Set Theory Book PDF

Author : Herbert B. Enderton
Publisher : Academic Press
Page : 279 pages
File Size : 52,7 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.

Descriptive Set Theory and Forcing

Arnold W. Miller
Descriptive Set Theory and Forcing Book PDF

Author : Arnold W. Miller
Publisher : Cambridge University Press
Page : 135 pages
File Size : 49,8 Mb
Release : 2017-05-18
Category : Mathematics
ISBN : 9781107168060

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Descriptive Set Theory and Forcing by Arnold W. Miller Pdf

These notes develop the theory of descriptive sets, leading up to a new proof of Louveau's separation theorem for analytic sets. A first course in mathematical logic and set theory is assumed, making this book suitable for advanced students and researchers.

Set Theory

Daniel W. Cunningham
Set Theory Book PDF

Author : Daniel W. Cunningham
Publisher : Cambridge University Press
Page : 265 pages
File Size : 52,8 Mb
Release : 2016-07-18
Category : Mathematics
ISBN : 9781107120327

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Set Theory by Daniel W. Cunningham Pdf

Set theory can be considered a unifying theory for mathematics. This book covers the fundamentals of the subject.

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 : 42,8 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.

Set Theory, Arithmetic, and Foundations of Mathematics

Juliette Kennedy,Roman Kossak
Set Theory Arithmetic and Foundations of Mathematics Book PDF

Author : Juliette Kennedy,Roman Kossak
Publisher : Cambridge University Press
Page : 242 pages
File Size : 52,9 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.

The Geometry of René Descartes

René Descartes
The Geometry of Ren Descartes Book PDF

Author : René Descartes
Publisher : Courier Corporation
Page : 272 pages
File Size : 50,9 Mb
Release : 2012-09-19
Category : Mathematics
ISBN : 9780486158174

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The Geometry of René Descartes by René Descartes Pdf

The great work that founded analytical geometry. Includes the original French text, Descartes' own diagrams, and the definitive Smith-Latham translation. "The greatest single step ever made in the progress of the exact sciences." — John Stuart Mill.