Mathematical Logic
From the Introduction: "We shall base our discussion on a set-theoretical foundation like that used in developing analysis, or algebra, or topology. We may consider our task as that of giving a mathematical analysis of the basic concepts of logic and mathematics themselves. Thus we treat mathem...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
1976, 1976
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| Edition: | 1st ed. 1976 |
| Series: | Graduate Texts in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- Interdependence of sections
- I Recursive Function Theory
- I. Turing machines
- 2. Elementary recursive and primitive recursive functions
- 3. Recursive functions; Turing computability
- 4. Markov algorithms
- 5. Recursion theory
- 6. Recursively enumerable sets
- 7. Survey of recursion theory
- II Elements of Logic
- 8. Sentential logic
- 9. Boolean algebra
- 10. Syntactics of first-order languages
- 11. Some basic results of first-order logic
- 12. Cylindric algebras
- III Decidable and Undecidable Theories
- 13. Some decidable theories
- 14. Implicit definability in number theories
- 15. General theory of undecidability
- 16. Some undecidable theories
- 17. Unprovability of consistency
- IV Model Theory
- 18. Construction of models
- 19. Elementary equivalence
- 20. Nonstandard mathematics
- 21. Complete theories
- 22. The interpolation theorem
- 23. Generalized products
- 24. Equational logic
- 25. Preservation and characterization theorems
- 26. Elementary classes and elementary equivalence
- 27. Types
- 28. Saturated structures
- V Unusual Logics
- 29. Inessential variations
- 30. Finitary extensions
- 31. Infinitary extensions
- Index of symbols
- Index of names and definitions