Mathematical Logic
Series: Oxford Texts in Logic; 3;
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Product details:
- Publisher OUP Oxford
- Date of Publication 17 May 2007
- ISBN 9780198571001
- Binding Hardback
- No. of pages258 pages
- Size 246x177x17 mm
- Weight 643 g
- Language English
- Illustrations halftones and figures 0
Categories
Short description:
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.
MoreLong description:
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.
Mathematical Logic is crisply written and is a pleasure to read. ..Chiswell and Hodges' book is at the very top of the reading list.
Table of Contents:
Preface
Prelude
Informal natural deduction
Propositional logic
First interlude: Wason's Selection Task
Quantifier-free logic
Second interlude: The Linda Problem
First-order logic
Postlude
The natural deduction rules
Denotational semantics
Solutions to some exercises
Index
