The Mathematics of Logic Paperback: A Guide to Completeness Theorems and Their Applications

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9780521708777: The Mathematics of Logic Paperback: A Guide to Completeness Theorems and Their Applications

Undergraduate textbook covering the key material for a typical first course in logic, including a full mathematical account of the most important result in logic, the Completeness Theorem for first-order logic. The author ensures that the number of new concepts at each stage is manageable, whilst providing lively mathematical applications throughout.

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"Kaye (pure mathematics, U. of Birmingham) gives undergraduate and first-year graduates key materials for a first course in logic, including a full mathematical account of the Completeness Theorem for first-order logic. As he builds a series of systems increasing in complexity, and proving and discussing the Completeness Theorem for each, Kaye keeps unfamiliar terminology to a minimum and provides proofs of all the required set theoretical results. He covers K<:o>nig's Lemma (including two ways of looking at mathematics), posets and maximal elements (including order), formal systems (including post systems and compatibility as bonuses), deduction in posets (including proving statements about a poset), Boolean algebras, propositional logic (including a system for proof about propositions), valuations (including semantics for propositional logic), filters and ideals (including the algebraic theory of Boolean algebras), first-order logic, completeness and compactness, model theory (including countable models) and nonstandard analysis (including infinitesimal numbers)." --Book News

About the Author:

Richard Kaye is a senior lecturer in pure mathematics at the University of Birmingham.

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ISBN 10: 052170877X ISBN 13: 9780521708777
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Descripción Paperback. Estado de conservación: New. This Book is in Good Condition; Customer Satisfaction Comes First.Delivery Time 4-12 days. 100% Money back Guaranteed!!!. Nº de ref. de la librería 052170877x

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Descripción CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2007. Paperback. Estado de conservación: New. 228 x 152 mm. Language: English . Brand New Book. 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 Konig 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. Nº de ref. de la librería AAA9780521708777

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Descripción Cambridge University Press, 2007. Estado de conservación: New. Brand New, Unread Copy in Perfect Condition. A+ Customer Service! Summary: Preface; How to read this book; 1. Knigs lemma; 2. Posets and maximal elements; 3. Formal systems; 4. Deductions in posets; 5. Boolean algebras; 6. Propositional logic; 7. Valuations; 8. Filters and ideals; 9. First-order logic; 10. Completeness and compactness; 11. Model theory; 12. Nonstandard analysis; Bibliography; Index. Nº de ref. de la librería ABE_book_new_052170877X

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Descripción CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2007. Paperback. Estado de conservación: New. 228 x 152 mm. Language: English . Brand New Book. 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 Konig 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. Nº de ref. de la librería AAA9780521708777

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Editorial: Cambridge University Press, New Delhi, India (2007)
ISBN 10: 052170877X ISBN 13: 9780521708777
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Descripción Cambridge University Press, New Delhi, India, 2007. Paperback. Estado de conservación: New. First Edition. 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. • Lively mathematical examples and some unusual formal systems stimulate the reader from the very beginning • Suitable as an introduction to logic for students without any background in formal set theory • Supported by companion web-pages containing further material and exercises Contents Preface; How to read this book; 1. König’s lemma; 2. Posets and maximal elements; 3. Formal systems; 4. Deductions in posets; 5. Boolean algebras; 6. Propositional logic; 7. Valuations; 8. Filters and ideals; 9. First-order logic; 10. Completeness and compactness; 11. Model theory; 12. Nonstandard analysis; Bibliography; Index. Printed Pages: 216 with 4 line diagrams, 141 exercises, and 50 worked examples. Size: 150 x 230 Mm. Nº de ref. de la librería 020838

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Descripción Cambridge University Press. Paperback. Estado de conservación: new. BRAND NEW, The Mathematics of Logic: A Guide to Completeness Theorems and Their Applications, Richard W. Kaye, 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 Konig'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. Nº de ref. de la librería B9780521708777

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Kaye
Editorial: Cambridge University Press, New Delhi, India (2007)
ISBN 10: 052170877X ISBN 13: 9780521708777
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Descripción Cambridge University Press, New Delhi, India, 2007. Paperback. Estado de conservación: New. First Edition. 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. ?Lively mathematical examples and some unusual formal systems stimulate the reader from the very beginning ?Suitable as an introduction to logic for students without any background in formal set theory ?Supported by companion web-pages containing further material and exercises Contents Preface; How to read this book; 1. König’s lemma; 2. Posets and maximal elements; 3. Formal systems; 4. Deductions in posets; 5. Boolean algebras; 6. Propositional logic; 7. Valuations; 8. Filters and ideals; 9. First-order logic; 10. Completeness and compactness; 11. Model theory; 12. Nonstandard analysis; Bibliography; Index. Printed Pages: 216 with 4 line diagrams, 141 exercises, and 50 worked examples. Size: 150 x 230 Mm. Nº de ref. de la librería 020838

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Descripción Estado de conservación: New. Bookseller Inventory # ST052170877X. Nº de ref. de la librería ST052170877X

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Descripción Cambridge University Press, 2007. PAP. Estado de conservación: New. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Nº de ref. de la librería FM-9780521708777

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