Mathematical Logic / by J.D. Monk.

Format:

Book

Author/Creator:

Monk, J.D., author.

Contributor:

SpringerLink (Online service)

Series:

Graduate texts in mathematics 2197-5612 ; 37.

Graduate Texts in Mathematics, 2197-5612 ; 37

Language:

English

Subjects (All):

Logic, Symbolic and mathematical.

Mathematical Logic and Foundations.

Local Subjects:

Mathematical Logic and Foundations.

Physical Description:

1 online resource (X, 532 pages).

Edition:

First edition 1976.

Contained In:

Springer Nature eBook

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 1976.

System Details:

text file PDF

Summary:

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.

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.

Other Format:

Printed edition:

ISBN:

9781468494525

Access Restriction:

Restricted for use by site license.