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An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof (Applied Logic Series, 27) - Hardcover
Synopsis
In case you are considering to adopt this book for courses with over 50 students, please contact ties.nijssen@springer.com for more information.
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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An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof
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An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof
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Kluwer Academic Publishers, Dordrecht, The Netherlands, 2002
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Hardcover. Condition: Very good. Applied Logic Series 27. xviii, 389 p. 24 cm. B&w figures. Some light soiling to exterior. Seller Inventory # 135811
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An Introduction to Mathematical Logic and Type Theory: To Truth Through Proof (Applied Logic Series, Band 27)
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An Introduction to Mathematical Logic and Type Theory
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Gebunden. Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Facilitates proofs of the classical incompleteness and undecidability theorems which are very elegant and easy to understandThe discussion of semantics makes clear the important distinction between standard and nonstandard models which is so important i. Seller Inventory # 4092087
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Condition: New. An introduction to mathematical logic that starts with propositional calculus and first-order logic. It is 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. Series: Applied Logic Series. Num Pages: 390 pages, biography. BIC Classification: PBCD. Category: (P) Professional & Vocational; (UP) Postgraduate, Research & Scholarly; (UU) Undergraduate. Dimension: 242 x 160 x 28. Weight in Grams: 772. . 2002. 2nd ed. 2002. Hardback. . . . . Seller Inventory # V9781402007637
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