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## Introduction to mathematical logic / Elliott Mendelson.

Editor: London : Chapman & Hall, 1997Edición: 4th edDescripción: x, 440 p. ; 24 cmISBN: 0412808307Otra clasificación: 03-01
Contenidos:
```1 The propositional calculus 
1.1 Propositional connectives. Truth tables 
1.2 Tautologies 
1.3 Adequate sets of connectives 
1.4 An axiom system for the propositional calculus 
1.5 Independence. Many-valued logics 
1.6 Other axiomatizations 
2 Quantification theory 
2.1 Quantifiers 
2.2 First-order languages and their interpretations. Satisfiability and truth. Models 
2.3 First-order theories 
2.4 Properties of first-order theories 
2.5 Additional metatheorems and derived rules 
2.6 Rule C 
2.7 Completeness theorems 
2.8 First-order theories with equality 
2.9 Definitions of new function letters and individual constants 
2.10 Prenex normal forms 
2.11 Isomorphism of interpretations. Categoricity of theories 
2.12 Generalized first-order theories. Completeness and decidability 
2.13 Elementary equivalence. Elementary extensions 
2.14 Ultrapowers. Non-standard analysis 
2.15 Semantic trees 
2.16 Quantification theory allowing empty domains 
3 Formal number theory 
3.1 An axiom system 
3.2 Number-theoretic functions and relations 
3.3 Primitive recursive and recursive functions 
3.4 Arithmetization. Gödel numbers 
3.5 The fixed-point theorem. Gödel’s incompleteness theorem 
3.6 Recursive undecidability. Church’s theorem 
4 Axiomatic set theory 
4.1 An axiom system 
4.2 Ordinal numbers 
4.3 Equinumerosity. Finite and denumerable sets 
4.4 Hartogs’ theorem. Initial ordinals. Ordinal arithmetic 
4.5 The axiom of choice. The axiom of regularity 
4.6 Other axiomatizations of set theory 
5 Computability 
5.1 Algorithms. Turing machines 
5.2 Diagrams 
5.3 Partial recursive functions. Unsolvable problems. 
5.4 The Kleene-Mostovski hierarchy. Recursively enumerable sets 
5.5 Other notions of computability 
5.6 Decision problems 
Appendix Second-order logic 
Bibliography 
Notation 
Index ``` Average rating: 0.0 (0 votes)
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Incluye referencias bibliográficas (p. -423) e índices.

1 The propositional calculus  --
1.1 Propositional connectives. Truth tables  --
1.2 Tautologies  --
1.3 Adequate sets of connectives  --
1.4 An axiom system for the propositional calculus  --
1.5 Independence. Many-valued logics  --
1.6 Other axiomatizations  --
2 Quantification theory  --
2.1 Quantifiers  --
2.2 First-order languages and their interpretations. Satisfiability and truth. Models  --
2.3 First-order theories  --
2.4 Properties of first-order theories  --
2.5 Additional metatheorems and derived rules  --
2.6 Rule C  --
2.7 Completeness theorems  --
2.8 First-order theories with equality  --
2.9 Definitions of new function letters and individual constants  --
2.10 Prenex normal forms  --
2.11 Isomorphism of interpretations. Categoricity of theories  --
2.12 Generalized first-order theories. Completeness and decidability  --
2.13 Elementary equivalence. Elementary extensions  --
2.14 Ultrapowers. Non-standard analysis  --
2.15 Semantic trees  --
2.16 Quantification theory allowing empty domains  --
3 Formal number theory  --
3.1 An axiom system  --
3.2 Number-theoretic functions and relations  --
3.3 Primitive recursive and recursive functions  --
3.4 Arithmetization. Gödel numbers  --
3.5 The fixed-point theorem. Gödel’s incompleteness theorem  --
3.6 Recursive undecidability. Church’s theorem  --
4 Axiomatic set theory  --
4.1 An axiom system  --
4.2 Ordinal numbers  --
4.3 Equinumerosity. Finite and denumerable sets  --
4.4 Hartogs’ theorem. Initial ordinals. Ordinal arithmetic  --
4.5 The axiom of choice. The axiom of regularity  --
4.6 Other axiomatizations of set theory  --
5 Computability  --
5.1 Algorithms. Turing machines  --
5.2 Diagrams  --
5.3 Partial recursive functions. Unsolvable problems.  --
5.4 The Kleene-Mostovski hierarchy. Recursively enumerable sets  --
5.5 Other notions of computability  --
5.6 Decision problems  --
Appendix Second-order logic  --
Answers to selected exercises  --
Bibliography  --
Notation  --
Index  --

MR, 99b:03002

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