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Introduction to Mathematical Logic and Type Theory To Truth Through Proof

ISBN-10: 1402007639
ISBN-13: 9781402007637
Edition: 2nd 2002 (Revised)
Authors: Peter B. Andrews
List price: $169.00 Buy it from $121.43
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Description: This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas,  More...

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Book details

List price: $169.00
Edition: 2nd
Copyright year: 2002
Publisher: Springer
Publication date: 7/31/2002
Binding: Hardcover
Pages: 390
Size: 6.50" wide x 9.50" long x 1.00" tall
Weight: 1.738
Language: English

This introduction to mathematical logic starts with propositional calculus and first-order logic. Topics covered include syntax, semantics, soundness, completeness, independence, normal forms, vertical paths through negation normal formulas, compactness, Smullyan's Unifying Principle, natural deduction, cut-elimination, semantic tableaux, Skolemization, Herbrand's Theorem, unification, duality, interpolation, and definability. The last three chapters of the book provide an introduction to type theory (higher-order logic). It is shown how various mathematical concepts can be formalized in this very expressive formal language. This expressive notation facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understand. The discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important in understanding puzzling phenomena such as the incompleteness theorems and Skolem's Paradox about countable models of set theory. Some of the numerous exercises require giving formal proofs. A computer program called ETPS which is available from the web facilitates doing and checking such exercises. Audience: This volume will be of interest to mathematicians, computer scientists, and philosophers in universities, as well as to computer scientists in industry who wish to use higher-order logic for hardware and software specification and verification.

Preface to the Second Edition
Preface
Introduction
Propositional Calculus
The Language of P
Supplement on Induction
The Axiomatic Structure of P
Semantics, Consistency, and Completeness of P
Independence
Propositional Connectives
Compactness
Ground Resolution
First-Order Logic
The Language of F
The Axiomatic Structure of F
Prenex Normal Form
Semantics of F
Independence
Abstract Consistency and Completeness
Supplement: Simplified Completeness Proof
Equality
Provability and Refutability
Natural Deduction
Gentzen's Theorem
Semantic Tableaux
Skolemization
Refutations of Universal Sentences
Herbrand's Theorem
Unification
Further Topics in First-Order Logic
Duality
Craig's Interpolation Theorem
Beth's Definability Theorem
Type Theory
Introduction
The Primitive Basis of Q[subscript 0]
Elementary Logic in Q[subscript 0]
Equality and Descriptions
Semantics of Q[subscript 0]
Completeness of Q[subscript 0]
Formalized Number Theory
Cardinal Numbers and the Axiom of Infinity
Peano's Postulates
Order
Minimization
Recursive Functions
Primitive Recursive Functions and Relations
Incompleteness and Undecidability
Godel Numbering
Godel's Incompleteness Theorems
Essential Incompleteness
Undecidability and Undefinability
Epilogue
Supplementary Exercises
Summary of Theorems
Bibliography
List of Figures
Index

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