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Mathematical Logic

Chiswell, Ian Hodges Wilfrid
Innbundet / 2007 / Engelsk

Produktdetaljer

ISBN
9780198571001
Publisert
2007
Utgiver
Vendor
Oxford University Press
Vekt
643 gr
Høyde
246 mm
Bredde
177 mm
Dybde
17 mm
Aldersnivå
UU, UP, P, 05, 06
Språk
Product language
Engelsk
Format
Product format
Innbundet
Antall sider
258

Forfatter
Chiswell, Ian
Hodges Wilfrid

Om bidragsyterne

Ian Chiswell acheived a Ph.D. at the University of Michigan in 1973 on the Bass-Serre theory of groups acting on trees. After three years as a temporary lecturer at the University of Birmingham he moved back to Queen Mary, University of London in 1976. His teaching experience dates back to 1968 when he was a teaching fellow at the University of Michigan. He spent the academic year 1972-73 in Germany at the Ruhr-Universitaet Bochum. He has published a monograph on lamda-trees, which are generalisations of ordinary trees. His work has connections with mathematical logic, mainly via non-standard free groups. Wilfrid Hodges achieved his DPhil at Oxford in 1970 for a thesis in model theory (mathematical logic). He has taught mathematics at London University for nearly forty years, first at Bedford College and then at Queen Mary, and also taught for visiting years in Los Angeles and Boulder (USA). Besides this book, he has four other textbooks of logic in print, at levels ranging from popular to research. He has served as president of the British Logic Colloquium and the European Association for Logic, Language and Information, and as vice-president of the London Mathematical Society.

Mathematical Logic

Chiswell, Ian Hodges Wilfrid
Innbundet / 2007 / Engelsk
Chiswell, Ian Hodges Wilfrid
Innbundet / 2007 / Engelsk
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Mathematical Logic is crisply written and is a pleasure to read. ..Chiswell and Hodges' book is at the very top of the reading list.

Michael Berg, MAA Online

The text is clearly laid out and written in an easy-to-read free-flowing style.

Times Higher Education Supplement

Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic. At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics. Alongside the practical examples, readers learn what can and can't be calculated; for example the correctness of a derivation proving a given sequent can be tested mechanically, but there is no general mechanical test for the existence of a derivation proving the given sequent. The undecidability results are proved rigorously in an optional final chapter, assuming Matiyasevich's theorem characterising the computably enumerable relations. Rigorous proofs of the adequacy and completeness proofs of the relevant logics are provided, with careful attention to the languages involved. Optional sections discuss the classification of mathematical structures by first-order theories; the required theory of cardinality is developed from scratch. Throughout the book there are notes on historical aspects of the material, and connections with linguistics and computer science, and the discussion of syntax and semantics is influenced by modern linguistic approaches. Two basic themes in recent cognitive science studies of actual human reasoning are also introduced. Including extensive exercises and selected solutions, this text is ideal for students in Logic, Mathematics, Philosophy, and Computer Science.
Les mer
Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic.
Les mer
Preface ; 1. Prelude ; 2. Informal natural deduction ; 3. Propositional logic ; 4. First interlude: Wason's Selection Task ; 5. Quantifier-free logic ; 6. Second interlude: The Linda Problem ; 7. First-order logic ; 8. Postlude ; A. The natural deduction rules ; B. Denotational semantics ; C. Solutions to some exercises ; Index
Les mer
Based on the authors' extensive teaching on the subject Practical examples are given for each idea as it is introduced Methods and concepts are introduced intuitively in terms of actual mathematical practice, but then developed rigorously Extensive exercises are presented along with selected solutions
Les mer
Ian Chiswell acheived a Ph.D. at the University of Michigan in 1973 on the Bass-Serre theory of groups acting on trees. After three years as a temporary lecturer at the University of Birmingham he moved back to Queen Mary, University of London in 1976. His teaching experience dates back to 1968 when he was a teaching fellow at the University of Michigan. He spent the academic year 1972-73 in Germany at the Ruhr-Universitaet Bochum. He has published a monograph on lamda-trees, which are generalisations of ordinary trees. His work has connections with mathematical logic, mainly via non-standard free groups. Wilfrid Hodges achieved his DPhil at Oxford in 1970 for a thesis in model theory (mathematical logic). He has taught mathematics at London University for nearly forty years, first at Bedford College and then at Queen Mary, and also taught for visiting years in Los Angeles and Boulder (USA). Besides this book, he has four other textbooks of logic in print, at levels ranging from popular to research. He has served as president of the British Logic Colloquium and the European Association for Logic, Language and Information, and as vice-president of the London Mathematical Society.
Les mer
Based on the authors' extensive teaching on the subject Practical examples are given for each idea as it is introduced Methods and concepts are introduced intuitively in terms of actual mathematical practice, but then developed rigorously Extensive exercises are presented along with selected solutions
Les mer

Relaterte produkter

Mathematical Logic is crisply written and is a pleasure to read. ..Chiswell and Hodges' book is at the very top of the reading list.

Michael Berg, MAA Online

The text is clearly laid out and written in an easy-to-read free-flowing style.

Times Higher Education Supplement

Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic. At each stage of the text, the reader is given an intuition based on standard mathematical practice, which is subsequently developed with clean formal mathematics. Alongside the practical examples, readers learn what can and can't be calculated; for example the correctness of a derivation proving a given sequent can be tested mechanically, but there is no general mechanical test for the existence of a derivation proving the given sequent. The undecidability results are proved rigorously in an optional final chapter, assuming Matiyasevich's theorem characterising the computably enumerable relations. Rigorous proofs of the adequacy and completeness proofs of the relevant logics are provided, with careful attention to the languages involved. Optional sections discuss the classification of mathematical structures by first-order theories; the required theory of cardinality is developed from scratch. Throughout the book there are notes on historical aspects of the material, and connections with linguistics and computer science, and the discussion of syntax and semantics is influenced by modern linguistic approaches. Two basic themes in recent cognitive science studies of actual human reasoning are also introduced. Including extensive exercises and selected solutions, this text is ideal for students in Logic, Mathematics, Philosophy, and Computer Science.
Les mer
Assuming no previous study in logic, this informal yet rigorous text covers the material of a standard undergraduate first course in mathematical logic, using natural deduction and leading up to the completeness theorem for first-order logic.
Les mer
Preface ; 1. Prelude ; 2. Informal natural deduction ; 3. Propositional logic ; 4. First interlude: Wason's Selection Task ; 5. Quantifier-free logic ; 6. Second interlude: The Linda Problem ; 7. First-order logic ; 8. Postlude ; A. The natural deduction rules ; B. Denotational semantics ; C. Solutions to some exercises ; Index
Les mer
Based on the authors' extensive teaching on the subject Practical examples are given for each idea as it is introduced Methods and concepts are introduced intuitively in terms of actual mathematical practice, but then developed rigorously Extensive exercises are presented along with selected solutions
Les mer
Ian Chiswell acheived a Ph.D. at the University of Michigan in 1973 on the Bass-Serre theory of groups acting on trees. After three years as a temporary lecturer at the University of Birmingham he moved back to Queen Mary, University of London in 1976. His teaching experience dates back to 1968 when he was a teaching fellow at the University of Michigan. He spent the academic year 1972-73 in Germany at the Ruhr-Universitaet Bochum. He has published a monograph on lamda-trees, which are generalisations of ordinary trees. His work has connections with mathematical logic, mainly via non-standard free groups. Wilfrid Hodges achieved his DPhil at Oxford in 1970 for a thesis in model theory (mathematical logic). He has taught mathematics at London University for nearly forty years, first at Bedford College and then at Queen Mary, and also taught for visiting years in Los Angeles and Boulder (USA). Besides this book, he has four other textbooks of logic in print, at levels ranging from popular to research. He has served as president of the British Logic Colloquium and the European Association for Logic, Language and Information, and as vice-president of the London Mathematical Society.
Les mer
Based on the authors' extensive teaching on the subject Practical examples are given for each idea as it is introduced Methods and concepts are introduced intuitively in terms of actual mathematical practice, but then developed rigorously Extensive exercises are presented along with selected solutions
Les mer

Produktdetaljer

ISBN
9780198571001
Publisert
2007
Utgiver
Vendor
Oxford University Press
Vekt
643 gr
Høyde
246 mm
Bredde
177 mm
Dybde
17 mm
Aldersnivå
UU, UP, P, 05, 06
Språk
Product language
Engelsk
Format
Product format
Innbundet
Antall sider
258

Forfatter
Chiswell, Ian
Hodges Wilfrid

Om bidragsyterne

Ian Chiswell acheived a Ph.D. at the University of Michigan in 1973 on the Bass-Serre theory of groups acting on trees. After three years as a temporary lecturer at the University of Birmingham he moved back to Queen Mary, University of London in 1976. His teaching experience dates back to 1968 when he was a teaching fellow at the University of Michigan. He spent the academic year 1972-73 in Germany at the Ruhr-Universitaet Bochum. He has published a monograph on lamda-trees, which are generalisations of ordinary trees. His work has connections with mathematical logic, mainly via non-standard free groups. Wilfrid Hodges achieved his DPhil at Oxford in 1970 for a thesis in model theory (mathematical logic). He has taught mathematics at London University for nearly forty years, first at Bedford College and then at Queen Mary, and also taught for visiting years in Los Angeles and Boulder (USA). Besides this book, he has four other textbooks of logic in print, at levels ranging from popular to research. He has served as president of the British Logic Colloquium and the European Association for Logic, Language and Information, and as vice-president of the London Mathematical Society.

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