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Mathematical Logic

ISBN-10: 0199215626

ISBN-13: 9780199215621

Edition: 2007

Authors: Ian Chiswell, Wilfrid Hodges

List price: $71.00
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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.
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Book details

List price: $71.00
Copyright year: 2007
Publisher: Oxford University Press, Incorporated
Publication date: 7/12/2007
Binding: Paperback
Pages: 260
Size: 6.65" wide x 9.37" long x 0.47" tall
Weight: 1.144
Language: English

Informal natural deduction
Propositional logic
First interlude: Wason's Selection Task
Quantifier-free logic
Second interlude: The Linda Problem
First-order logic
The natural deduction rules
Denotational semantics
Solutions to some exercises