Mathematical LogicFrom 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
| 1 | |
| 6 | |
| 14 | |
Elementary recursive and primitive recursive functions | 26 |
Recursive functions Turing computability | 45 |
4 Markov algorithms | 69 |
Recursion theory | 76 |
Recursively enumerable sets | 92 |
Part IV | 309 |
Construction of models | 311 |
Elementary equivalence | 327 |
20 Nonstandard mathematics | 341 |
Complete theories | 349 |
The interpolation theorem | 365 |
23 Generalized products | 376 |
Equational logic | 384 |
Survey of recursion theory | 105 |
Part II | 112 |
Elements of Logic | 113 |
8 Sentential logic | 115 |
9 Boolean algebra | 141 |
Syntactics of firstorder languages | 162 |
Some basic results of firstorder logic | 194 |
Cylindric algebras | 219 |
Some decidable theories | 233 |
Implicit definability in number theories | 244 |
General theory of undecidability | 262 |
Some undecidable theories | 279 |
Unprovability of consistency | 298 |
Preservation and characterization theorems | 393 |
Elementary classes and elementary equivalence | 406 |
Types | 441 |
Saturated structures | 454 |
Part V | 470 |
Unusual Logics | 471 |
Inessential variations | 473 |
Finitary extensions | 488 |
Infinitary extensions | 504 |
| 521 | |
| 525 | |
Other editions - View all
Common terms and phrases
A₁ algorithm assume atomic axiomatizable axioms B₁ BA's binary relation Boolean algebras cardinal choose Clearly completeness theorem conditions are equivalent consistent contradiction Corollary countable deduction theorem Definition desired easily effective element f(xo finite sequence finite subset first-order language Fmla Fmlag formula function f function mapping g(xo Gödel number Hence homomorphism individual constants infinite intuitive isomorphism L-structure Lemma Let f let ƒ Löwenheim-Skolem theorem m-ary Markov algorithm mathematical n-ary nonempty nonlogical constants notation notion obtained Obviously occur one-one function operation symbol partial recursive function Piel primitive recursive functions PROOF prove quantifier recursively enumerable sentential logic set of sentences Subf suppose syntactically definable T₁ tautology Turing computable Turing machine ultrafilter ultraproducts unary relation symbol undecidable v₁ v₂ variables x₁