Lectures In Logic And Set Theory Volume 1 Mathematical Logic

Author : George Tourlakis
Publisher : Cambridge University Press
Page : 344 pages
File Size : 45,8 Mb
Release : 2003-01-09
Category : Mathematics
ISBN : 9781139439428

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Lectures in Logic and Set Theory: Volume 1, Mathematical Logic by George Tourlakis Pdf

This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. Volume 1 includes formal proof techniques, a section on applications of compactness (including nonstandard analysis), a generous dose of computability and its relation to the incompleteness phenomenon, and the first presentation of a complete proof of Godel's 2nd incompleteness since Hilbert and Bernay's Grundlagen theorem.

Author : George J. Tourlakis
Publisher : Unknown
Page : 328 pages
File Size : 47,5 Mb
Release : 2003
Category : Electronic books
ISBN : 1107128560

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Mathematical Logic by George J. Tourlakis Pdf

Author : George Tourlakis
Publisher : Cambridge University Press
Page : 596 pages
File Size : 45,9 Mb
Release : 2003-02-13
Category : Mathematics
ISBN : 113943943X

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

This two-volume work bridges the gap between introductory expositions of logic or set theory on one hand, and the research literature on the other. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly conversational lecture style that makes them equally effective for self-study or class use. 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 will provide the reader with a solid foundation in set theory and provides a context for the presentation of advanced topics such as absoluteness, relative consistency results, two expositions of Godel's constructible universe, numerous ways of viewing recursion, and a chapter on Cohen forcing.

Author : George Tourlakis
Publisher : Cambridge University Press
Page : 0 pages
File Size : 50,6 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).

Author : Hao Wang
Publisher : Courier Corporation
Page : 292 pages
File Size : 49,5 Mb
Release : 2014-09-22
Category : Mathematics
ISBN : 9780486171043

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Popular Lectures on Mathematical Logic by Hao Wang Pdf

Noted logician discusses both theoretical underpinnings and practical applications, exploring set theory, model theory, recursion theory and constructivism, proof theory, logic's relation to computer science, and other subjects. 1981 edition, reissued by Dover in 1993 with a new Postscript by the author.

Author : George Tourlakis
Publisher : Unknown
Page : 128 pages
File Size : 47,6 Mb
Release : 2003
Category : Electronic
ISBN : OCLC:909215820

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Lectures in Logic and Set Theory by George Tourlakis Pdf

Author : Robert R. Stoll
Publisher : Courier Corporation
Page : 512 pages
File Size : 45,8 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 : Michael L. O'Leary
Publisher : John Wiley & Sons
Page : 464 pages
File Size : 55,6 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.

Author : Jerzy Słupecki,Ludwik Borkowski
Publisher : Pergamon
Page : 374 pages
File Size : 45,5 Mb
Release : 1967
Category : Mathematics
ISBN : UOM:39015078124834

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Elements of Mathematical Logic and Set Theory by Jerzy Słupecki,Ludwik Borkowski Pdf

Author : Jerzy Słupecki,Ludwik Borkowski
Publisher : Pergamon
Page : 372 pages
File Size : 42,5 Mb
Release : 1967
Category : Mathematics
ISBN : UCAL:B4396227

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Elements of Mathematical Logic and Set Theory by Jerzy Słupecki,Ludwik Borkowski Pdf

Author : George Tourlakis
Publisher : Cambridge University Press
Page : 0 pages
File Size : 42,8 Mb
Release : 2003-02-13
Category : Mathematics
ISBN : 0521753740

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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).

Author : Elliott Mendelson
Publisher : CRC Press
Page : 464 pages
File Size : 51,6 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.

Author : Iqbal H. Jebril,Hemen Dutta,Ilwoo Cho
Publisher : CRC Press
Page : 160 pages
File Size : 43,5 Mb
Release : 2021-10
Category : Logic, Symbolic and mathematical
ISBN : 1032106220

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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"--

Author : George Tourlakis
Publisher : John Wiley & Sons
Page : 314 pages
File Size : 52,5 Mb
Release : 2011-03-01
Category : Mathematics
ISBN : 9781118030691

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Mathematical Logic by George Tourlakis Pdf

A comprehensive and user-friendly guide to the use of logic in mathematical reasoning Mathematical Logic presents a comprehensive introduction to formal methods of logic and their use as a reliable tool for deductive reasoning. With its user-friendly approach, this book successfully equips readers with the key concepts and methods for formulating valid mathematical arguments that can be used to uncover truths across diverse areas of study such as mathematics, computer science, and philosophy. The book develops the logical tools for writing proofs by guiding readers through both the established "Hilbert" style of proof writing, as well as the "equational" style that is emerging in computer science and engineering applications. Chapters have been organized into the two topical areas of Boolean logic and predicate logic. Techniques situated outside formal logic are applied to illustrate and demonstrate significant facts regarding the power and limitations of logic, such as: Logic can certify truths and only truths. Logic can certify all absolute truths (completeness theorems of Post and Gödel). Logic cannot certify all "conditional" truths, such as those that are specific to the Peano arithmetic. Therefore, logic has some serious limitations, as shown through Gödel's incompleteness theorem. Numerous examples and problem sets are provided throughout the text, further facilitating readers' understanding of the capabilities of logic to discover mathematical truths. In addition, an extensive appendix introduces Tarski semantics and proceeds with detailed proofs of completeness and first incompleteness theorems, while also providing a self-contained introduction to the theory of computability. With its thorough scope of coverage and accessible style, Mathematical Logic is an ideal book for courses in mathematics, computer science, and philosophy at the upper-undergraduate and graduate levels. It is also a valuable reference for researchers and practitioners who wish to learn how to use logic in their everyday work.

Author : P. T. Johnstone
Publisher : Cambridge University Press
Page : 128 pages
File Size : 54,8 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.