Introduction to Mathematical Logic and Type Theory To Truth Through Proof

Name: Introduction to Mathematical Logic and Type Theory To Truth Through Proof
Price: 37.73 USD
Availability: InStock
ISBN: 9781402007637

ISBN-10: 1402007639

ISBN-13: 9781402007637

Edition: 2nd 2002 (Revised)

Authors: Peter B. Andrews

List price: $139.99

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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, 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…

Book details

List price: $139.99
Edition: 2nd
Copyright year: 2002
Publisher: Springer Netherlands
Publication date: 7/31/2002
Binding: Hardcover
Pages: 390
Size: 6.30" wide x 9.45" long x 1.00" tall
Weight: 3.652
Language: English



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