Introduction to Mathematical Logic and Type Theory To Truth Through Proof
Edition: 2nd 2002 (Revised)
List price: $169.00
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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 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.
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All the information you need in one place! Each Study Brief is a summary of one specific subject; facts, figures, and explanations to help you learn faster.
List price: $169.00
Copyright year: 2002
Publication date: 7/31/2002
Size: 6.50" wide x 9.50" long x 1.00" tall
|Preface to the Second Edition|
|The Language of P|
|Supplement on Induction|
|The Axiomatic Structure of P|
|Semantics, Consistency, and Completeness of P|
|The Language of F|
|The Axiomatic Structure of F|
|Prenex Normal Form|
|Semantics of F|
|Abstract Consistency and Completeness|
|Supplement: Simplified Completeness Proof|
|Provability and Refutability|
|Refutations of Universal Sentences|
|Further Topics in First-Order Logic|
|Craig's Interpolation Theorem|
|Beth's Definability Theorem|
|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|
|Primitive Recursive Functions and Relations|
|Incompleteness and Undecidability|
|Godel's Incompleteness Theorems|
|Undecidability and Undefinability|
|Summary of Theorems|
|List of Figures|