Mathematical logic
著者
書誌事項
Mathematical logic
（Graduate texts in mathematics, 37）
Springer-Verlag, 1976
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注記
Includes bibliographies and indexes
内容説明・目次
内容説明
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 mathematical and logical practice as given empirical data and attempt to develop a purely mathematical theory of logic abstracted from these data."
There are 31 chapters in 5 parts and approximately 320 exercises marked by difficulty and whether or not they are necessary for further work in the book.
目次
- 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.
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