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## Introduction to mathematical logic / by Elliott Mendelson.

Editor: Princeton, New Jersey : D. Van Nostrand, 1964Descripción: x, 300 p. ; 24 cmOtra clasificación: 03-01
Contenidos:
```1. THE PROPOSITIONAL CALCULUS [12]
1. Propositional Connectives. Truth Tables [12]
2. Tautologies [17]
3. Adequate Sets of Connectives [24]
4. An Axiom System for the Propositional Calculus [29]
5. Independence. Many-Valued Logics [38]
6. Other Axiomatizations [40]
2. QUANTIFICATION THEORY [45]
1. Quantifiers [45]
2. Interpretations. Satisfiability and Truth. Models [49]
3. First-Order Theories [56]
4. Properties of First-Order Theories [59]
5. Completeness Theorems [62]
7. Rule C [73]
8. First-Order Theories with Equality [75]
9. Definitions of New Function Letters and Individual Constants [82]
10. Prenex Normal Forms [85]
11. Isomorphism of Interpretations. Categoricity of Theories [90]
12. Generalized First-Order Theories. Completeness and Decidability [92]
3. FORMAL NUMBER THEORY [102]
1. An Axiom System [102]
2. Number-Theoretic Functions and Relations [117]
3. Primitive Recursive and Recursive Functions [120]
4. Arithmetization. Gödel Numbers [135]
5. Godel’s Theorem for S [142]
6. Recursive Undecidability. Tarski’s Theorem. Robinson’s System [150]
4. AXIOMATIC SET THEORY [159]
1. An Axiom System [159]
2. Ordinal Numbers [170]
3. Equinumerosity. Finite and Denumerable Sets [180]
4. Hartogs' Theorem. Initial Ordinals. Ordinal Arithmetic [187]
5. The Axiom of Choice. The Axiom of Restriction [197]
5. EFFECTIVE COMPUTABILITY [207]
1. Markov Algorithms [207]
2. Turing Algorithms [229]
3. Herbrand-Gödel Computability. Recursively Enumerable Sets [238]
4. Undecidable Problems [254]
APPENDIX: A CONSISTENCY PROOF FOR FORMAL NUMBER THEORY [258]
BIBLIOGRAPHY [272]
INDEX [291]
```
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1. THE PROPOSITIONAL CALCULUS [12] --
1. Propositional Connectives. Truth Tables [12] --
2. Tautologies [17] --
3. Adequate Sets of Connectives [24] --
4. An Axiom System for the Propositional Calculus [29] --
5. Independence. Many-Valued Logics [38] --
6. Other Axiomatizations [40] --
2. QUANTIFICATION THEORY [45] --
1. Quantifiers [45] --
2. Interpretations. Satisfiability and Truth. Models [49] --
3. First-Order Theories [56] --
4. Properties of First-Order Theories [59] --
5. Completeness Theorems [62] --
6. Some Additional Metatheorems [70] --
7. Rule C [73] --
8. First-Order Theories with Equality [75] --
9. Definitions of New Function Letters and Individual Constants [82] --
10. Prenex Normal Forms [85] --
11. Isomorphism of Interpretations. Categoricity of Theories [90] --
12. Generalized First-Order Theories. Completeness and Decidability [92] --
3. FORMAL NUMBER THEORY [102] --
1. An Axiom System [102] --
2. Number-Theoretic Functions and Relations [117] --
3. Primitive Recursive and Recursive Functions [120] --
4. Arithmetization. Gödel Numbers [135] --
5. Godel’s Theorem for S [142] --
6. Recursive Undecidability. Tarski’s Theorem. Robinson’s System [150] --
4. AXIOMATIC SET THEORY [159] --
1. An Axiom System [159] --
2. Ordinal Numbers [170] --
3. Equinumerosity. Finite and Denumerable Sets [180] --
4. Hartogs' Theorem. Initial Ordinals. Ordinal Arithmetic [187] --
5. The Axiom of Choice. The Axiom of Restriction [197] --
5. EFFECTIVE COMPUTABILITY [207] --
1. Markov Algorithms [207] --
2. Turing Algorithms [229] --
3. Herbrand-Gödel Computability. Recursively Enumerable Sets [238] --
4. Undecidable Problems [254] --
APPENDIX: A CONSISTENCY PROOF FOR FORMAL NUMBER THEORY [258] --
BIBLIOGRAPHY [272] --
INDEX [291] --

MR, 29 #2158

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