Mathematical Logic

J. D. Monk

ISBN 10: 0387901701 / ISBN 13: 9780387901701

Editore: Springer New York, Springer US Sep 1976, 1976

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Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 548 pp. Englisch.

Codice articolo 9780387901701

Dati bibliografici

• Titolo: Mathematical Logic
• Editore: Springer New York, Springer US Sep 1976
• Data di pubblicazione: 1976
• Lingua: Inglese
• ISBN 10: 0387901701
• ISBN 13: 9780387901701
• Rilegatura: Buch
• Condizione: Neu
• Dimensioni: 241 L x 160 A x 34 P (millimetri) 241 millimetri di larghezza per 160 millimetri di altezza per 34 millimetri di profondità
• Peso: 980 grammi

Descrizione articolo

Riassunto

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."

Contenuti

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.