Mathematical Logic by J.D. Monk (English) Hardcover Book

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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."

FORMATHardcover LANGUAGEEnglish CONDITIONBrand New Publisher Description

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.

Table of Contents

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.

Long Description

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.

Details ISBN0387901701 Series Graduate Texts in Mathematics Language English ISBN-10 0387901701 ISBN-13 9780387901701 Media Book Format Hardcover Series Number 37 Year 1976 Imprint Springer-Verlag New York Inc. Place of Publication New York, NY Country of Publication United States Birth 1930 Short Title MATHEMATICAL LOGIC 1976/E Pages 532 Illustrations X, 532 p. DOI 10.1007/b31287;10.1007/978-1-4684-9452-5 AU Release Date 1976-09-07 NZ Release Date 1976-09-07 US Release Date 1976-09-07 UK Release Date 1976-09-07 Author J.D. Monk Publisher Springer-Verlag New York Inc. Edition Description 1976 ed. Edition 1976th Publication Date 1976-09-07 Alternative 9781468494549 DEWEY 510 Audience General We've got this

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