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Graduate Texts in Mathematics Ser.: Mathematical Logic by J. D. Monk (1976, Hardcover)

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About this product

Product Identifiers

PublisherSpringer New York

ISBN-100387901701

ISBN-139780387901701

eBay Product ID (ePID)1390465

Product Key Features

Number of PagesX, 532 Pages

Publication NameMathematical Logic

LanguageEnglish

SubjectLogic

Publication Year1976

TypeTextbook

Subject AreaMathematics

AuthorJ. D. Monk

SeriesGraduate Texts in Mathematics Ser.

FormatHardcover

Dimensions

Item Weight73.4 Oz

Item Length9.2 in

Item Width6.1 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN75-042416

Series Volume Number37

Number of Volumes1 vol.

IllustratedYes

Table Of ContentInterdependence 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.

SynopsisFrom 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.

LC Classification NumberQA8.9-10.3