A Course In Mathematical Logic For Mathematicians
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Logic Of Mathematics
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Author : Zofia Adamowicz
language : en
Publisher: John Wiley & Sons
Release Date : 2011-09-26
Logic Of Mathematics written by Zofia Adamowicz and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-26 with Mathematics categories.
A thorough, accessible, and rigorous presentation of the central theorems of mathematical logic . . . ideal for advanced students of mathematics, computer science, and logic Logic of Mathematics combines a full-scale introductory course in mathematical logic and model theory with a range of specially selected, more advanced theorems. Using a strict mathematical approach, this is the only book available that contains complete and precise proofs of all of these important theorems: * Gödel's theorems of completeness and incompleteness * The independence of Goodstein's theorem from Peano arithmetic * Tarski's theorem on real closed fields * Matiyasevich's theorem on diophantine formulas Logic of Mathematics also features: * Full coverage of model theoretical topics such as definability, compactness, ultraproducts, realization, and omission of types * Clear, concise explanations of all key concepts, from Boolean algebras to Skolem-Löwenheim constructions and other topics * Carefully chosen exercises for each chapter, plus helpful solution hints At last, here is a refreshingly clear, concise, and mathematically rigorous presentation of the basic concepts of mathematical logic-requiring only a standard familiarity with abstract algebra. Employing a strict mathematical approach that emphasizes relational structures over logical language, this carefully organized text is divided into two parts, which explain the essentials of the subject in specific and straightforward terms. Part I contains a thorough introduction to mathematical logic and model theory-including a full discussion of terms, formulas, and other fundamentals, plus detailed coverage of relational structures and Boolean algebras, Gödel's completeness theorem, models of Peano arithmetic, and much more. Part II focuses on a number of advanced theorems that are central to the field, such as Gödel's first and second theorems of incompleteness, the independence proof of Goodstein's theorem from Peano arithmetic, Tarski's theorem on real closed fields, and others. No other text contains complete and precise proofs of all of these theorems. With a solid and comprehensive program of exercises and selected solution hints, Logic of Mathematics is ideal for classroom use-the perfect textbook for advanced students of mathematics, computer science, and logic.
Logic For Mathematicians
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Author : J. Barkley Rosser
language : en
Publisher: Courier Dover Publications
Release Date : 2008-12-18
Logic For Mathematicians written by J. Barkley Rosser and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-18 with Mathematics categories.
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.
The Mathematics Of Logic
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Author : Richard W. Kaye
language : en
Publisher: Cambridge University Press
Release Date : 2007-07-12
The Mathematics Of Logic written by Richard W. Kaye and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-12 with Mathematics categories.
This undergraduate textbook covers the key material for a typical first course in logic, in particular presenting a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. Looking at a series of interesting systems, increasing in complexity, then proving and discussing the Completeness Theorem for each, the author ensures that the number of new concepts to be absorbed at each stage is manageable, whilst providing lively mathematical applications throughout. Unfamiliar terminology is kept to a minimum, no background in formal set-theory is required, and the book contains proofs of all the required set theoretical results. The reader is taken on a journey starting with König's Lemma, and progressing via order relations, Zorn's Lemma, Boolean algebras, and propositional logic, to completeness and compactness of first-order logic. As applications of the work on first-order logic, two final chapters provide introductions to model theory and nonstandard analysis.
A Profile Of Mathematical Logic
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Author : Howard DeLong
language : en
Publisher: Courier Corporation
Release Date : 2004-06-17
A Profile Of Mathematical Logic written by Howard DeLong and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-17 with Philosophy categories.
Anyone seeking a readable and relatively brief guide to logic can do no better than this classic introduction. A treat for both the intellect and the imagination, it profiles the development of logic from ancient to modern times and compellingly examines the nature of logic and its philosophical implications. No prior knowledge of logic is necessary; readers need only an acquaintance with high school mathematics. The author emphasizes understanding, rather than technique, and focuses on such topics as the historical reasons for the formation of Aristotelian logic, the rise of mathematical logic after more than 2,000 years of traditional logic, the nature of the formal axiomatic method and the reasons for its use, and the main results of metatheory and their philosophic import. The treatment of the Gödel metatheorems is especially detailed and clear, and answers to the problems appear at the end.
Mathematical Logic
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Author : J.D. Monk
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Mathematical Logic written by J.D. Monk and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
From the Introduction: "We shall base our discussion on a set-theoretical foundation like that used in developing analysis, or algebra, or topology. We may consider our task as that of giving a mathematical analysis of the basic concepts of logic and mathematics themselves. Thus we treat mathematical and logical practice as given empirical data and attempt to develop a purely mathematical theory of logic abstracted from these data." There are 31 chapters in 5 parts and approximately 320 exercises marked by difficulty and whether or not they are necessary for further work in the book.
Basic Concepts Of Mathematics And Logic
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Author : Michael C. Gemignani
language : en
Publisher: Courier Corporation
Release Date : 2004-01-01
Basic Concepts Of Mathematics And Logic written by Michael C. Gemignani and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-01-01 with Mathematics categories.
This text emphasizes logic and the theory of sets. Students who take no further courses in the field will find it an excellent resource for developing an appreciation for the nature of mathematics. Others will discover the foundations for future studies — set theory, logic, counting, numbers, functions, and more. 1968 edition. 43 figures. 25 tables.
Mathematical Logic
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Author : H.-D. Ebbinghaus
language : en
Publisher: Springer Science & Business Media
Release Date : 1996-11-15
Mathematical Logic written by H.-D. Ebbinghaus and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-11-15 with Mathematics categories.
This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.
Mathematics And Logic
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Author : Mark Kac
language : en
Publisher: Courier Corporation
Release Date : 1992-01-01
Mathematics And Logic written by Mark Kac and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Philosophy categories.
Fascinating study of the origin and nature of mathematical thought, including relation of mathematics and science, 20th-century developments, impact of computers, and more.Includes 34 illustrations. 1968 edition."
First Course In Mathematical Logic
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Author : Patrick Suppes
language : en
Publisher: Courier Corporation
Release Date : 2012-04-30
First Course In Mathematical Logic written by Patrick Suppes and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-30 with Mathematics categories.
Rigorous introduction is simple enough in presentation and context for wide range of students. Symbolizing sentences; logical inference; truth and validity; truth tables; terms, predicates, universal quantifiers; universal specification and laws of identity; more.
Logic And Discrete Mathematics
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Author : Willem Conradie
language : en
Publisher: John Wiley & Sons
Release Date : 2015-05-08
Logic And Discrete Mathematics written by Willem Conradie and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-08 with Mathematics categories.
Solutions manual to accompany Logic and Discrete Mathematics: A Concise Introduction This book features a unique combination of comprehensive coverage of logic with a solid exposition of the most important fields of discrete mathematics, presenting material that has been tested and refined by the authors in university courses taught over more than a decade. Written in a clear and reader-friendly style, each section ends with an extensive set of exercises, most of them provided with complete solutions which are available in this accompanying solutions manual.