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Mathematical Logic (Dover Books on Mathematics)
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Located in: Harrisburg, Pennsylvania, United States
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eBay item number:135052136278
Item specifics
- Condition
- Release Year
- 2002
- Book Title
- Mathematical Logic (Dover Books on Mathematics)
- ISBN
- 9780486425337
- Publication Name
- Mathematical Logic
- Item Length
- 8.7in
- Publisher
- Dover Publications, Incorporated
- Series
- Dover Books on Mathematics Ser.
- Publication Year
- 2002
- Type
- Textbook
- Format
- Hardcover
- Language
- English
- Item Height
- 0.9in
- Item Width
- 5.5in
- Item Weight
- 16 Oz
- Number of Pages
- 416 Pages
About this product
Product Information
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.
Product Identifiers
Publisher
Dover Publications, Incorporated
ISBN-10
0486425339
ISBN-13
9780486425337
eBay Product ID (ePID)
2263056
Product Key Features
Publication Name
Mathematical Logic
Format
Hardcover
Language
English
Series
Dover Books on Mathematics Ser.
Publication Year
2002
Type
Textbook
Number of Pages
416 Pages
Dimensions
Item Length
8.7in
Item Height
0.9in
Item Width
5.5in
Item Weight
16 Oz
Additional Product Features
Lc Classification Number
Qa9
Edition Description
Unabridged Edition
Table of Content
PART I. ELEMENTARY MATHEMATICAL LOGICCHAPTER 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 symbolsCHAPTER III. THE PREDICATE CALCULUS WITH EQUALITY 28. "Functions, terms" 29. Equality 30. "Equality vs. equivalence, extensionality" 31. DescriptionsPART II. MATHEMATICAL LOGIC AND THE FOUNDATIONS OF MATHEMATICSCHAPTER 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 systemsCHAPTER 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"BIBLIOGRAPHYTHEOREM AND LEMMA NUMBERS: PAGESLIST OF POSTULATESSYMBOLS AND NOTATIONSINDEX
Copyright Date
2002
Target Audience
College Audience
Topic
History & Philosophy, Logic
Lccn
2002-034823
Dewey Decimal
510/.01
Dewey Edition
21
Illustrated
Yes
Genre
Mathematics
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eBay item number:135052136278
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