Mathematical Logic

Häftad, Engelska, 2003

369 kr

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Undergraduate 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.

Produktinformation

Utgivningsdatum2003-03-28
Mått136 x 214 x 20 mm
Vikt420 g
FormatHäftad
SpråkEngelska
SerieDover Books on Mathema 1.4tics
Antal sidor432
FörlagDover Publications Inc.
ISBN9780486425337

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Matematik inom Naturvetenskap och teknik

PART I. ELEMENTARY MATHEMATICAL LOGICCHAPTER I. THE PROPOSITIONAL CALCULUS1. Linguistic considerations: formulas2. "Model theory: truth tables,validity "3. "Model theory: the substitution rule, a collection of valid formulas"4. Model theory: implication and equivalence5. Model theory: chains of equivalences6. Model theory: duality7. Model theory: valid consequence8. Model theory: condensed truth tables9. Proof theory: provability and deducibility10. Proof theory: the deduction theorem11. "Proof theory: consistency, introduction and elimination rules"12. Proof theory: completeness13. Proof theory: use of derived rules14. Applications to ordinary language: analysis of arguments15. Applications to ordinary language: incompletely stated arguments CHAPTER II. THE PREDICATE CALCULUS16. "Linguistic considerations: formulas, free and bound occurrences of variables"17. "Model theory: domains, validity"18. Model theory: basic results on validity19. Model theory: further results on validity20. Model theory: valid consequence21. Proof theory: provability and deducibility22. Proof theory: the deduction theorem23. "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 symbolsCHAPTER III. THE PREDICATE CALCULUS WITH EQUALITY28. "Functions, terms"29. Equality30. "Equality vs. equivalence, extensionality"31. DescriptionsPART II. MATHEMATICAL LOGIC AND THE FOUNDATIONS OF MATHEMATICSCHAPTER IV. THE FOUNDATIONS OF MATHEMATICS32. Countable sets33. Cantor's diagonal method34. Abstract sets35. The paradoxes36. Axiomatic thinking vs. intuitive thinking in mathematics37. "Formal systems, metamathematics"38. Formal number theory39. Some other formal systemsCHAPTER V. COMPUTABILITY AND DECIDABILITY40. Decision and computation procedures41. "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: introduction49. Gödel's completeness theorem: the basic discovery50. "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 arithmetic54. Gentzen's theorem55. "Permutability, Herbrand's theorem"56. Craig's interpolation theorem57. "Beth's theorem on definability, Robinson's consistency theorem"BIBLIOGRAPHYTHEOREM AND LEMMA NUMBERS: PAGESLIST OF POSTULATESSYMBOLS AND NOTATIONSINDEX