Mathematical Logic / by J. Donald Monk
(Graduate Texts in Mathematics ; 37)
| データ種別 | 電子ブック |
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| 出版者 | New York, NY : Springer New York : Imprint: Springer |
| 出版年 | 1976 |
| 本文言語 | 英語 |
| 大きさ | X, 532 p : online resource |
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| 内容注記 | 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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| 一般注記 | 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 |
| 著者標目 | *Monk, J. Donald author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Mathematical logic FREE:Mathematics FREE:Mathematical Logic and Foundations |
| 分 類 | DC23:511.3 |
| 巻冊次 | ISBN:9781468494525 
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| ISBN | 9781468494525 |
| URL | http://dx.doi.org/10.1007/978-1-4684-9452-5 |
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