Introduction to mathematical logic / by Elliott Mendelson.
Series The university series in undergraduate mathematicsEditor: Princeton, New Jersey : D. Van Nostrand, 1964Descripción: x, 300 p. ; 24 cmOtra clasificación: 03-011. 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]
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03 M478 Aristotle's modal syllogisms / | 03 M537 Introduction to mathematical logic / | 03 M537 Introduction to mathematical logic / | 03 M537 Introduction to mathematical logic / | 03 M537-4 Introduction to mathematical logic / | 03 M636 Logica matematica : | 03 M6365 An introduction to model theory / |
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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