Author | Grzegorczyk, Andrzej. author |
---|---|
Title | An Outline of Mathematical Logic [electronic resource] : Fundamental Results and Notions Explained with all Details / by Andrzej Grzegorczyk |
Imprint | Dordrecht : Springer Netherlands, 1974 |
Connect to | http://dx.doi.org/10.1007/978-94-010-2112-8 |
Descript | 606 p. online resource |
to the Problems of the Foundations of Mathematics -- 1. Mathematical Domains -- 2. Examples of Mathematical Domains -- 3. Selected Kinds of Relations and Functions -- 4. Logical Analysis of Mathematical Concepts -- 5. Zermeloโs Set Theory -- 6. Set-Theoretical Approach to Relations and Functions -- 7. The Genetic Construction of Natural Numbers -- 8. Expansion of the Concept of Number -- 9. Construction of New Mathematical Domains -- 10. Subdomains, Homomorphisms, Isomorphisms -- 11. Products. Real Numbers -- I. The Classical Logical Calculus -- 1. The Classical Characteristics of the Sentential Connectives -- 2. Tautologies in the Classical Sentential Calculus and Their Applications to Certain Mathematical Considerations -- 3. An Axiomatic Approach to the Sentential Calculus -- 4. The Classical Concept of Quantifier -- 5. The Predicate Calculus in the Traditional Interpretation -- 6. Reduction of Quantifier Rules to Axioms, c.l.c Tautologies True in the Empty Domain -- 7. The Concepts of Consequence and Theory. Applications of the Logical Calculus to the Formalization of Mathematical Theories -- 8. The Logical Functional Calculus L* and Its Applications to the Formalization of Theories with Functions -- 9. Certain Syntactic Properties of the Classical Logical Calculus -- 10. On Definitions -- II. Models of Axiomatic Theories -- 1. The Concept of Satisfaction -- 2. The Concepts of Truth and Model. The Properties of the Set of Sentences True in a Model -- 3. Existence of co-complete Extensions and Denumerable Models -- 4. Some Other Concepts and Results in Model Theory -- 5. Skolemโs Elimination of Quantifiers, Consistency of Compound Theories and Interpolation Theorems -- 6. Definability -- III. Logical Hierarchy of Concepts -- 1. The Concept of Effectiveness in Arithmetic -- 2. Some Properties of Computable Functions 417 -- 3. Effectiveness of Methods of Proof -- 4. Representability of Computable Relations in Arithmetic -- 5. Problems of Decidability -- 6. Logical Hierarchy of Arithmetic Concepts -- Supplement. a Historical Outline -- Index of Symbols -- Index of Names