Overview

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.

Full Product Details

Author:   J.D. Monk
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   1976 ed.
Volume:   37
Dimensions:   Width: 15.60cm , Height: 3.00cm , Length: 23.40cm
Weight:   2.080kg
ISBN:  

9780387901701

ISBN 10:   0387901701
Pages:   532
Publication Date:   07 September 1976
Audience:   General/trade ,  Professional and scholarly ,  General ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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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.

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