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.
Author(s): J. Donald Monk
Series: Graduate Texts in Mathematics 37
Edition: 1
Publisher: Springer
Year: 1976
Language: English
Commentary: new scan high resolution
Pages: 531
Tags: Mathematics, general
Front Matter....Pages i-x
Introduction....Pages 1-9
Front Matter....Pages 11-13
Turing Machines....Pages 14-25
Elementary recursive and primitive recursive functions....Pages 26-44
Recursive Functions; Turing Computability....Pages 45-68
Markov Algorithms....Pages 69-75
Recursion Theory....Pages 76-91
Recursively Enumerable Sets....Pages 92-104
Survey of Recursion Theory....Pages 105-111
Front Matter....Pages 113-114
Sentential Logic....Pages 115-140
Boolean Algebra....Pages 141-161
Syntactics of First-order Languages....Pages 162-193
Some Basic Results of First-order Logic....Pages 194-218
Cylindric Algebras....Pages 219-229
Front Matter....Pages 231-232
Some Decidable Theories....Pages 233-243
Implicit Definability in Number Theories....Pages 244-261
General Theory of Undecidability....Pages 262-278
Some Undecidable Theories....Pages 279-297
Unprovability of Consistency....Pages 298-308
Front Matter....Pages 309-310
Construction of Models....Pages 311-326
Elementary Equivalence....Pages 327-340
Front Matter....Pages 309-310
Nonstandard Mathematics....Pages 341-348
Complete Theories....Pages 349-364
The Interpolation Theorem....Pages 365-375
Generalized Products....Pages 376-383
Equational Logic....Pages 384-392
Preservation and Characterization Theorems....Pages 393-405
Elementary Classes and Elementary Equivalence....Pages 406-440
Types....Pages 441-453
Saturated Structures....Pages 454-469
Front Matter....Pages 471-472
Inessential Variations....Pages 473-487
Finitary Extensions....Pages 488-503
Infinitary Extensions....Pages 504-520
Back Matter....Pages 521-531
