An Outline of Mathematical Logic

An Outline of Mathematical Logic

Author: A. Grzegorczyk

Publisher: Springer Science & Business Media

Published: 2013-03-07

Total Pages: 604

ISBN-13: 9401022046

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Recent years have seen the appearance of many English-Ianguage hand books of logie and numerous monographs on topieal discoveries in the foundations of mathematies. These publications on the foundations of mathematies as a whole are rather difficult for the beginners or refer the reader to other handbooks and various pieeemeal eontribu tions and also sometimes to largely conceived "mathematical fol klore" of unpublished results. As distinct from these, the present book is as easy as possible systematic exposition of the now classical results in the foundations of mathematics. Henee the book may be useful especially for those readers who want to have all the proofs carried out in full and all the concepts explained in detail. In this sense the book is self-contained. The reader's ability to guess is not assumed, and the author's ambition was to reduce the use of sueh words as evident and obvious in proofs to aminimum. This is why the book, it is believed, may be helpful in teaehing or learning the foundation of mathematics in those situations in which the student cannot refer to a parallel lecture on the subject. This is also the reason that I do not insert in the book the last results and the most modem and fashionable approaches to the subjeet, which does not enrich the essential knowledge in founda tions but ean discourage the beginner by their abstract form. A. G.


Book Synopsis An Outline of Mathematical Logic by : A. Grzegorczyk

Download or read book An Outline of Mathematical Logic written by A. Grzegorczyk and published by Springer Science & Business Media. This book was released on 2013-03-07 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent years have seen the appearance of many English-Ianguage hand books of logie and numerous monographs on topieal discoveries in the foundations of mathematies. These publications on the foundations of mathematies as a whole are rather difficult for the beginners or refer the reader to other handbooks and various pieeemeal eontribu tions and also sometimes to largely conceived "mathematical fol klore" of unpublished results. As distinct from these, the present book is as easy as possible systematic exposition of the now classical results in the foundations of mathematics. Henee the book may be useful especially for those readers who want to have all the proofs carried out in full and all the concepts explained in detail. In this sense the book is self-contained. The reader's ability to guess is not assumed, and the author's ambition was to reduce the use of sueh words as evident and obvious in proofs to aminimum. This is why the book, it is believed, may be helpful in teaehing or learning the foundation of mathematics in those situations in which the student cannot refer to a parallel lecture on the subject. This is also the reason that I do not insert in the book the last results and the most modem and fashionable approaches to the subjeet, which does not enrich the essential knowledge in founda tions but ean discourage the beginner by their abstract form. A. G.

An Outline of Mathematical Logic

An Outline of Mathematical Logic

Author: A. Grzegorczyk

Publisher:

Published: 2014-01-15

Total Pages: 608

ISBN-13: 9789401022057

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Book Synopsis An Outline of Mathematical Logic by : A. Grzegorczyk

Download or read book An Outline of Mathematical Logic written by A. Grzegorczyk and published by . This book was released on 2014-01-15 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Outline of Mathematical Logic

An Outline of Mathematical Logic

Author: Andrzej Grzegorczyk

Publisher: Springer

Published: 2011-12-10

Total Pages: 606

ISBN-13: 9789401021135

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Recent years have seen the appearance of many English-language hand books of logic and numerous monographs on topical discoveries in the foundations of mathematics. These publications on the foundations of mathematics as a whole are rather difficult for the beginners or refer the reader to other handbooks and various piecemeal contribu tions and also sometimes to largely conceived "mathematical fol klore" of unpublished results. As distinct from these, the present book is as easy as possible systematic exposition of the now classical results in the foundations of mathematics. Hence the book may be useful especially for those readers who want to have all the proofs carried out in full and all the concepts explained in detail. In this sense the book is self-contained. The reader's ability to guess is not assumed, and the author's ambition was to reduce the use of such words as evident and obvious in proofs to a minimum. This is why the book, it is believed, may be helpful in teaching or learning the foundation of mathematics in those situations in which the student cannot refer to a parallel lecture on the subject. This is also the reason that I do not insert in the book the last results and the most modem and fashionable approaches to the subject, which does not enrich the essential knowledge in founda tions but can discourage the beginner by their abstract form. A. G.


Book Synopsis An Outline of Mathematical Logic by : Andrzej Grzegorczyk

Download or read book An Outline of Mathematical Logic written by Andrzej Grzegorczyk and published by Springer. This book was released on 2011-12-10 with total page 606 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent years have seen the appearance of many English-language hand books of logic and numerous monographs on topical discoveries in the foundations of mathematics. These publications on the foundations of mathematics as a whole are rather difficult for the beginners or refer the reader to other handbooks and various piecemeal contribu tions and also sometimes to largely conceived "mathematical fol klore" of unpublished results. As distinct from these, the present book is as easy as possible systematic exposition of the now classical results in the foundations of mathematics. Hence the book may be useful especially for those readers who want to have all the proofs carried out in full and all the concepts explained in detail. In this sense the book is self-contained. The reader's ability to guess is not assumed, and the author's ambition was to reduce the use of such words as evident and obvious in proofs to a minimum. This is why the book, it is believed, may be helpful in teaching or learning the foundation of mathematics in those situations in which the student cannot refer to a parallel lecture on the subject. This is also the reason that I do not insert in the book the last results and the most modem and fashionable approaches to the subject, which does not enrich the essential knowledge in founda tions but can discourage the beginner by their abstract form. A. G.

Mathematical Logic

Mathematical Logic

Author: Joseph R. Shoenfield

Publisher: CRC Press

Published: 2018-05-02

Total Pages: 281

ISBN-13: 135143330X

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This classic introduction to the main areas of mathematical logic provides the basis for a first graduate course in the subject. It embodies the viewpoint that mathematical logic is not a collection of vaguely related results, but a coherent method of attacking some of the most interesting problems, which face the mathematician. The author presents the basic concepts in an unusually clear and accessible fashion, concentrating on what he views as the central topics of mathematical logic: proof theory, model theory, recursion theory, axiomatic number theory, and set theory. There are many exercises, and they provide the outline of what amounts to a second book that goes into all topics in more depth. This book has played a role in the education of many mature and accomplished researchers.


Book Synopsis Mathematical Logic by : Joseph R. Shoenfield

Download or read book Mathematical Logic written by Joseph R. Shoenfield and published by CRC Press. This book was released on 2018-05-02 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic introduction to the main areas of mathematical logic provides the basis for a first graduate course in the subject. It embodies the viewpoint that mathematical logic is not a collection of vaguely related results, but a coherent method of attacking some of the most interesting problems, which face the mathematician. The author presents the basic concepts in an unusually clear and accessible fashion, concentrating on what he views as the central topics of mathematical logic: proof theory, model theory, recursion theory, axiomatic number theory, and set theory. There are many exercises, and they provide the outline of what amounts to a second book that goes into all topics in more depth. This book has played a role in the education of many mature and accomplished researchers.

A Friendly Introduction to Mathematical Logic

A Friendly Introduction to Mathematical Logic

Author: Christopher C. Leary

Publisher: Lulu.com

Published: 2015

Total Pages: 382

ISBN-13: 1942341075

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At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition's treatment of languages, structures, and deductions, leading to rigorous proofs of Gödel's First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises.


Book Synopsis A Friendly Introduction to Mathematical Logic by : Christopher C. Leary

Download or read book A Friendly Introduction to Mathematical Logic written by Christopher C. Leary and published by Lulu.com. This book was released on 2015 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: At the intersection of mathematics, computer science, and philosophy, mathematical logic examines the power and limitations of formal mathematical thinking. In this expansion of Leary's user-friendly 1st edition, readers with no previous study in the field are introduced to the basics of model theory, proof theory, and computability theory. The text is designed to be used either in an upper division undergraduate classroom, or for self study. Updating the 1st Edition's treatment of languages, structures, and deductions, leading to rigorous proofs of Gödel's First and Second Incompleteness Theorems, the expanded 2nd Edition includes a new introduction to incompleteness through computability as well as solutions to selected exercises.

A Mathematical Introduction to Logic

A Mathematical Introduction to Logic

Author: Herbert B. Enderton

Publisher: Elsevier

Published: 2001-01-23

Total Pages: 330

ISBN-13: 0080496466

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A Mathematical Introduction to Logic


Book Synopsis A Mathematical Introduction to Logic by : Herbert B. Enderton

Download or read book A Mathematical Introduction to Logic written by Herbert B. Enderton and published by Elsevier. This book was released on 2001-01-23 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Mathematical Introduction to Logic

Introduction to Mathematical Logic

Introduction to Mathematical Logic

Author: Elliot Mendelsohn

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 351

ISBN-13: 1461572886

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This is a compact mtroduction to some of the pnncipal tOpICS of mathematical logic . In the belief that beginners should be exposed to the most natural and easiest proofs, I have used free-swinging set-theoretic methods. The significance of a demand for constructive proofs can be evaluated only after a certain amount of experience with mathematical logic has been obtained. If we are to be expelled from "Cantor's paradise" (as nonconstructive set theory was called by Hilbert), at least we should know what we are missing. The major changes in this new edition are the following. (1) In Chapter 5, Effective Computability, Turing-computabIlity IS now the central notion, and diagrams (flow-charts) are used to construct Turing machines. There are also treatments of Markov algorithms, Herbrand-Godel-computability, register machines, and random access machines. Recursion theory is gone into a little more deeply, including the s-m-n theorem, the recursion theorem, and Rice's Theorem. (2) The proofs of the Incompleteness Theorems are now based upon the Diagonalization Lemma. Lob's Theorem and its connection with Godel's Second Theorem are also studied. (3) In Chapter 2, Quantification Theory, Henkin's proof of the completeness theorem has been postponed until the reader has gained more experience in proof techniques. The exposition of the proof itself has been improved by breaking it down into smaller pieces and using the notion of a scapegoat theory. There is also an entirely new section on semantic trees.


Book Synopsis Introduction to Mathematical Logic by : Elliot Mendelsohn

Download or read book Introduction to Mathematical Logic written by Elliot Mendelsohn and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a compact mtroduction to some of the pnncipal tOpICS of mathematical logic . In the belief that beginners should be exposed to the most natural and easiest proofs, I have used free-swinging set-theoretic methods. The significance of a demand for constructive proofs can be evaluated only after a certain amount of experience with mathematical logic has been obtained. If we are to be expelled from "Cantor's paradise" (as nonconstructive set theory was called by Hilbert), at least we should know what we are missing. The major changes in this new edition are the following. (1) In Chapter 5, Effective Computability, Turing-computabIlity IS now the central notion, and diagrams (flow-charts) are used to construct Turing machines. There are also treatments of Markov algorithms, Herbrand-Godel-computability, register machines, and random access machines. Recursion theory is gone into a little more deeply, including the s-m-n theorem, the recursion theorem, and Rice's Theorem. (2) The proofs of the Incompleteness Theorems are now based upon the Diagonalization Lemma. Lob's Theorem and its connection with Godel's Second Theorem are also studied. (3) In Chapter 2, Quantification Theory, Henkin's proof of the completeness theorem has been postponed until the reader has gained more experience in proof techniques. The exposition of the proof itself has been improved by breaking it down into smaller pieces and using the notion of a scapegoat theory. There is also an entirely new section on semantic trees.

A Concise Introduction to Mathematical Logic

A Concise Introduction to Mathematical Logic

Author: Wolfgang Rautenberg

Publisher: Springer Science & Business Media

Published: 2006-09-28

Total Pages: 273

ISBN-13: 0387342419

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While there are already several well known textbooks on mathematical logic this book is unique in treating the material in a concise and streamlined fashion. This allows many important topics to be covered in a one semester course. Although the book is intended for use as a graduate text the first three chapters can be understood by undergraduates interested in mathematical logic. The remaining chapters contain material on logic programming for computer scientists, model theory, recursion theory, Godel’s Incompleteness Theorems, and applications of mathematical logic. Philosophical and foundational problems of mathematics are discussed throughout the text.


Book Synopsis A Concise Introduction to Mathematical Logic by : Wolfgang Rautenberg

Download or read book A Concise Introduction to Mathematical Logic written by Wolfgang Rautenberg and published by Springer Science & Business Media. This book was released on 2006-09-28 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: While there are already several well known textbooks on mathematical logic this book is unique in treating the material in a concise and streamlined fashion. This allows many important topics to be covered in a one semester course. Although the book is intended for use as a graduate text the first three chapters can be understood by undergraduates interested in mathematical logic. The remaining chapters contain material on logic programming for computer scientists, model theory, recursion theory, Godel’s Incompleteness Theorems, and applications of mathematical logic. Philosophical and foundational problems of mathematics are discussed throughout the text.

An outline of mathematical logic

An outline of mathematical logic

Author: Andrzej Grzegorczyk

Publisher:

Published: 1974

Total Pages: 596

ISBN-13:

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Book Synopsis An outline of mathematical logic by : Andrzej Grzegorczyk

Download or read book An outline of mathematical logic written by Andrzej Grzegorczyk and published by . This book was released on 1974 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Introduction to Mathematical Logic

Introduction to Mathematical Logic

Author: Micha? Walicki

Publisher: World Scientific

Published: 2012

Total Pages: 281

ISBN-13: 9814343862

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This is a systematic and well-paced introduction to mathematical logic. Excellent as a course text, the book does not presuppose any previous knowledge and can be used also for self-study by more ambitious students. Starting with the basics of set theory, induction and computability, it covers propositional and first-order logic their syntax, reasoning systems and semantics. Soundness and completeness results for Hilbert's and Gentzen's systems are presented, along with simple decidability arguments. The general applicability of various concepts and techniques is demonstrated by highlighting their consistent reuse in different contexts. Unlike in most comparable texts, presentation of syntactic reasoning systems precedes the semantic explanations. The simplicity of syntactic constructions and rules of a high, though often neglected, pedagogical value aids students in approaching more complex semantic issues. This order of presentation also brings forth the relative independence of syntax from the semantics, helping to appreciate the importance of the purely symbolic systems, like those underlying computers. An overview of the history of logic precedes the main text, in which careful presentation of concepts, results and examples is accompanied by the informal analogies and illustrations. These informal aspects are kept clearly apart from the technical ones. Together, they form a unique text which may be appreciated equally by lecturers and students occupied with mathematical precision, as well as those interested in the relations of logical formalisms to the problems of computability and the philosophy of mathematical logic.


Book Synopsis Introduction to Mathematical Logic by : Micha? Walicki

Download or read book Introduction to Mathematical Logic written by Micha? Walicki and published by World Scientific. This book was released on 2012 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a systematic and well-paced introduction to mathematical logic. Excellent as a course text, the book does not presuppose any previous knowledge and can be used also for self-study by more ambitious students. Starting with the basics of set theory, induction and computability, it covers propositional and first-order logic their syntax, reasoning systems and semantics. Soundness and completeness results for Hilbert's and Gentzen's systems are presented, along with simple decidability arguments. The general applicability of various concepts and techniques is demonstrated by highlighting their consistent reuse in different contexts. Unlike in most comparable texts, presentation of syntactic reasoning systems precedes the semantic explanations. The simplicity of syntactic constructions and rules of a high, though often neglected, pedagogical value aids students in approaching more complex semantic issues. This order of presentation also brings forth the relative independence of syntax from the semantics, helping to appreciate the importance of the purely symbolic systems, like those underlying computers. An overview of the history of logic precedes the main text, in which careful presentation of concepts, results and examples is accompanied by the informal analogies and illustrations. These informal aspects are kept clearly apart from the technical ones. Together, they form a unique text which may be appreciated equally by lecturers and students occupied with mathematical precision, as well as those interested in the relations of logical formalisms to the problems of computability and the philosophy of mathematical logic.