About this product

Product Identifiers

PublisherDover Publications, Incorporated

ISBN-100486425339

ISBN-139780486425337

eBay Product ID (ePID)2263056

Product Key Features

Number of Pages432 Pages

LanguageEnglish

Publication NameMathematical Logic

Publication Year2002

SubjectHistory & Philosophy, Logic

TypeTextbook

Subject AreaMathematics

AuthorStephen Cole Kleene

SeriesDover Books on Mathematics Ser.

FormatTrade Paperback

Dimensions

Item Height0.9 in

Item Weight17.6 Oz

Item Length8.7 in

Item Width5.5 in

Additional Product Features

Intended AudienceCollege Audience

LCCN2002-034823

Dewey Edition21

IllustratedYes

Dewey Decimal510/.01

Table Of ContentPART I. ELEMENTARY MATHEMATICAL LOGIC CHAPTER I. THE PROPOSITIONAL CALCULUS 1. Linguistic considerations: formulas 2. "Model theory: truth tables,validity " 3. "Model theory: the substitution rule, a collection of valid formulas" 4. Model theory: implication and equivalence 5. Model theory: chains of equivalences 6. Model theory: duality 7. Model theory: valid consequence 8. Model theory: condensed truth tables 9. Proof theory: provability and deducibility 10. Proof theory: the deduction theorem 11. "Proof theory: consistency, introduction and elimination rules" 12. Proof theory: completeness 13. Proof theory: use of derived rules 14. Applications to ordinary language: analysis of arguments 15. Applications to ordinary language: incompletely stated arguments CHAPTER II. THE PREDICATE CALCULUS 16. "Linguistic considerations: formulas, free and bound occurrences of variables" 17. "Model theory: domains, validity" 18. Model theory: basic results on validity 19. Model theory: further results on validity 20. Model theory: valid consequence 21. Proof theory: provability and deducibility 22. Proof theory: the deduction theorem 23. "Proof theory: consistency, introduction and elimination rules" 24. "Proof theory: replacement, chains of equivalences" 25. "Proof theory: alterations of quantifiers, prenex form" 26. "Applications to ordinary language: sets, Aristotelian categorical forms" 27. Applications to ordinary language: more on translating words into symbols CHAPTER III. THE PREDICATE CALCULUS WITH EQUALITY 28. "Functions, terms" 29. Equality 30. "Equality vs. equivalence, extensionality" 31. Descriptions PART II. MATHEMATICAL LOGIC AND THE FOUNDATIONS OF MATHEMATICS CHAPTER IV. THE FOUNDATIONS OF MATHEMATICS 32. Countable sets 33. Cantor's diagonal method 34. Abstract sets 35. The paradoxes 36. Axiomatic thinking vs. intuitive thinking in mathematics 37. "Formal systems, metamathematics" 38. Formal number theory 39. Some other formal systems CHAPTER V. COMPUTABILITY AND DECIDABILITY 40. Decision and computation procedures 41. "Turing machines, Church's thesis" 42. Church's theorem (via Turing machines) 43. Applications to formal number theory: undecidability (Church) and incompleteness (Gödel's theorem) 44. Applications to formal number theory: consistency proofs (Gödel's second theorem) 45. "Application to the predicate calculus (Church, Turing)" 46. "Degrees of unsolvability (Post), hierarchies (Kleene, Mostowski)." 47. Undecidability and incompleteness using only simple consistency (Rosser) CHAPTER VI. THE PREDICATE CALCULUS (ADDITIONAL TOPICS) 48. Gödel's completeness theorem: introduction 49. Gödel's completeness theorem: the basic discovery 50. "Gödel's completeness theorem with a Gentzen-type formal system, the Löwenheim-Skolem theorem" 51. Gödel's completeness theorem (with a Hilbert-type formal system) 52. "Gödel's completeness theorem, and the Löwenheim-Skolem theorem, in the predicate calculus with equality" 53. Skolen's paradox and nonstandard models of arithmetic 54. Gentzen's theorem 55. "Permutability, Herbrand's theorem" 56. Craig's interpolation theorem 57. "Beth's theorem on definability, Robinson's consistency theorem" BIBLIOGRAPHY THEOREM AND LEMMA NUMBERS: PAGES LIST OF POSTULATES SYMBOLS AND NOTATIONS INDEX

Edition DescriptionUnabridged edition

SynopsisUndergraduate students with no prior instruction in mathematical logic will benefit from this multi-part text. Part I offers an elementary but thorough overview of mathematical logic of 1st order. Part II introduces some of the newer ideas and the more profound results of logical research in the 20th century. 1967 edition., Undergraduate students with no prior classroom instruction in mathematical logic will benefit from this evenhanded multipart text. It begins with an elementary but thorough overview of mathematical logic of first order. The treatment extends beyond a single method of formulating logic to offer instruction in a variety of techniques: model theory (truth tables), Hilbert-type proof theory, and proof theory handled through derived rules. The second part supplements the previously discussed material and introduces some of the newer ideas and the more profound results of twentieth-century logical research. Subsequent chapters explore the study of formal number theory, with surveys of the famous incompleteness and undecidability results of Godel, Church, Turing, and others. The emphasis in the final chapter reverts to logic, with examinations of Godel's completeness theorem, Gentzen's theorem, Skolem's paradox and nonstandard models of arithmetic, and other theorems. The author, Stephen Cole Kleene, was Cyrus C. MacDuffee Professor of Mathematics at the University of Wisconsin, Madison. Preface. Bibliography. Theorem and Lemma Numbers: Pages. List of Postulates. Symbols and Notations. Index.

LC Classification NumberQA9