Mathematical Logic (Paperback)

J.D. Monk

ISBN 10: 1468494546 / ISBN 13: 9781468494549

Editore: Springer-Verlag New York Inc., New York, NY, 2012

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Paperback. 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. 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." Shipping may be from multiple locations in the US or from the UK, depending on stock availability.

Codice articolo 9781468494549

Dati bibliografici

• Titolo: Mathematical Logic (Paperback)
• Editore: Springer-Verlag New York Inc., New York, NY
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 1468494546
• ISBN 13: 9781468494549
• Rilegatura: Paperback
• Condizione: new

Descrizione articolo

Riassunto

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.

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.