Mathematical Logic

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. 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