Introduction to Mathematical LogicPrinceton University Press, 1996 - 378 pàgines Logic is sometimes called the foundation of mathematics: the logician studies the kinds of reasoning used in the individual steps of a proof. Alonzo Church was a pioneer in the field of mathematical logic, whose contributions to number theory and the theories of algorithms and computability laid the theoretical foundations of computer science. His first Princeton book, The Calculi of Lambda-Conversion (1941), established an invaluable tool that computer scientists still use today. Even beyond the accomplishment of that book, however, his second Princeton book, Introduction to Mathematical Logic, defined its subject for a generation. Originally published in Princeton's Annals of Mathematics Studies series, this book was revised in 1956 and reprinted a third time, in 1996, in the Princeton Landmarks in Mathematics series. Although new results in mathematical logic have been developed and other textbooks have been published, it remains, sixty years later, a basic source for understanding formal logic. Church was one of the principal founders of the Association for Symbolic Logic; he founded the Journal of Symbolic Logic in 1936 and remained an editor until 1979 At his death in 1995, Church was still regarded as the greatest mathematical logician in the world. |
Continguts
INTRODUCTION | 1 |
Functions | 17 |
Some further theorems and metatheorems of P₂ | 22 |
Propositions and propositional functions | 23 |
Improper symbols connectives | 33 |
Operators quantifiers | 41 |
The logistic method | 49 |
Syntax | 59 |
The primitive basis of | 191 |
Derived rules of substitution | 193 |
Duality | 203 |
Prenex normal form | 211 |
The Pure Functional Calculus of First Order | 218 |
Skolem normal form | 225 |
Gödels completeness theorem | 233 |
The decision problem solution in special cases | 246 |
Semantics | 65 |
Some further theorems and metatheorems of P₁ | 91 |
Duality | 107 |
Independence | 113 |
Primitive connectives for the propositional calculus | 131 |
Partial systems of propositional calculus | 140 |
The Propositional Calculus Continued | 156 |
Historical notes | 159 |
Propositional calculus | 179 |
Consistency of | 185 |
Reductions of the decision problem | 271 |
Functional calculus of first order with equality | 281 |
Historical notes | 289 |
Functional Calculi of Second Order | 295 |
Exercises 54 | 315 |
Wellordering of the individuals | 341 |
Exercises 58 | 354 |
362 | |
374 | |
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Meaning and Grammar, second edition: An Introduction to Semantics Gennaro Chierchia,Sally Mcconnell-Ginet Previsualització no disponible - 2000 |