An Outline of Mathematical Logic: Fundamental Results and Notions Explained with all Details (Synthese Library, 70) [Softcover reprint of the original 1st ed. 1974] 9401021147, 9789401021142

Recent years have seen the appearance of many English-language hand books of logic and numerous monographs on topical d

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English Pages 606 [610] Year 2011

An Outline of Mathematical Logic: Fundamental Results and Notions Explained with all Details (Synthese Library, 70) [Softcover reprint of the original 1st ed. 1974]
9401021147, 9789401021142

Author / Uploaded
Andrzej Grzegorczyk

Categories
Mathematics
Logic

Table of contents :
Preface
Contents
Introduction 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. Zermelo's 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
Chapter 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 Oassical 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
Chapter 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 ω-complete Extensions and Denumerable Models
4. Some Other Concepts and Results in Model Theory
5. Skolem's Elimination of Quantifiers, Consistency of Compound Theories and Interpolation Theorems
6. Definability
Chapter III. Logical hierarchy of concepts
1. The Concept of Effectiveness in Arithmetic
2. Some Properties of Computable Functions
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
Bibliography
Index of symbols
Index of names
Subject index

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