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Mathematical logic and formalized theories : a survey of basic concepts and results /
Mathematical Logic and Formalized Theories.
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Amsterdam :
North-Holland,
[1974, 1971]
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Front Cover; Mathematical logic and Formalized Theories: A Survey of Basic Concepts and Results; Copyright Page; Dedication; PREFACE; Table of Contents; CHAPTER I. THE SENTENTIAL LOGIC; 1.1. Introduction; 1.2. Sentential Connectives; 1.3. The Sentential Logic P. Symbols and Formulas; 1.4. Tautologies; 1.5. Axiom Schemata of P. Rules of Inference and Theorems; 1.6. Metamathematical Properties of P; CHAPTER II. THE FIRST-ORDER PREDICATE LOGIC: I; 2.1. The First-Order Predicate Logic F1. Symbols, Quantifiers and Formulas; 2.2. Interpretations. Truth and Validity.
- 2.3. Axiom Schemata of F . Rules of Inference and Theorems. Consistency of F 2.4. The Deduction Theorem; CHAPTER III. THE FIRST-ORDER PREDICATE LOGIC: II; 3.1. Elementary Theories; 3.2. Completeness Theorems; 3.3. Further Corollaries. Decision Problem; 3.4. The First-Order Predicate Logic With Identity; 3.5. The First-Order Predicate Logic With Identity and Operation Symbols; CHAPTER IV. THE SECOND-ORDER PREDICATE LOGIC. THEORY OF DEFINITION; 4.1. Introduction; 4.2. The Second-Order Predicate Logic F2; 4.3. Second-Order Theories; 4.4. Theory of Definition; CHAPTER V. THE NATURAL NUMBERS.
- 5.1. Introduction5.2. Elementary Arithmetic: The Theory N; 5.3. The Metamathematics of N; 5.4. Second-Order Arithmetic: The Theory N2; 5.5. The Metamathematics of N2; CHAPTER VI. THE REAL NUMBERS; 6.1. The Theory R; 6.2. The Metamathematics of R and of Elementary Algebra; 6.3. Second-Order Real Number Theory: The Theory R2; 6.4. The Metamathematics of R2; CHAPTER VII. AXIOMATIC SET THEORY; 7.1. Paradoxes; 7.2. The Zermelo-Fraenkel Axioms; 7.3. The Axiom of Choice; 7.4. The Metamathematics of ZF; 7.5. Strengthened Forms of ZF; CHAPTER VIIII. NCOMPLETENESS. UNDECIDABILITY; 8.1. Introduction.
- 8.2. Recursive Functions and Relations. Representability8.3. Arithmetization; 8.4. G�odel's First Incompleteness Theorem; 8.5. G�odel's Second Incompleteness Theorem; 8.6. Tarski's Theorem; 8.7. Decision Problem. Church's Thesis. Recursively Enumerable Sets; 8.8. Undecidability; AUTHOR INDEX; SUBJECT INDEX.