Introduction to mathematical logic / Elliott Mendelson.
Editor: London : Chapman & Hall, 1997Edición: 4th edDescripción: x, 440 p. ; 24 cmISBN: 0412808307Otra clasificación: 03-011 The propositional calculus [11] 1.1 Propositional connectives. Truth tables [11] 1.2 Tautologies [15] 1.3 Adequate sets of connectives [27] 1.4 An axiom system for the propositional calculus [33] 1.5 Independence. Many-valued logics [43] 1.6 Other axiomatizations [45] 2 Quantification theory [50] 2.1 Quantifiers [50] 2.2 First-order languages and their interpretations. Satisfiability and truth. Models [56] 2.3 First-order theories [69] 2.4 Properties of first-order theories [71] 2.5 Additional metatheorems and derived rules [76] 2.6 Rule C [81] 2.7 Completeness theorems [84] 2.8 First-order theories with equality [94] 2.9 Definitions of new function letters and individual constants [103] 2.10 Prenex normal forms [106] 2.11 Isomorphism of interpretations. Categoricity of theories [111] 2.12 Generalized first-order theories. Completeness and decidability [113] 2.13 Elementary equivalence. Elementary extensions [123] 2.14 Ultrapowers. Non-standard analysis [129] 2.15 Semantic trees [141] 2.16 Quantification theory allowing empty domains [147] 3 Formal number theory [154] 3.1 An axiom system [154] 3.2 Number-theoretic functions and relations [170] 3.3 Primitive recursive and recursive functions [174] 3.4 Arithmetization. Gödel numbers [190] 3.5 The fixed-point theorem. Gödel’s incompleteness theorem [203] 3.6 Recursive undecidability. Church’s theorem [216] 4 Axiomatic set theory [225] 4.1 An axiom system [225] 4.2 Ordinal numbers [240] 4.3 Equinumerosity. Finite and denumerable sets [253] 4.4 Hartogs’ theorem. Initial ordinals. Ordinal arithmetic [263] 4.5 The axiom of choice. The axiom of regularity [275] 4.6 Other axiomatizations of set theory [287] 5 Computability [305] 5.1 Algorithms. Turing machines [305] 5.2 Diagrams [311] 5.3 Partial recursive functions. Unsolvable problems. [317] 5.4 The Kleene-Mostovski hierarchy. Recursively enumerable sets [333] 5.5 Other notions of computability [345] 5.6 Decision problems [361] Appendix Second-order logic [368] Answers to selected exercises [383] Bibliography [412] Notation [424] Index [427]
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Incluye referencias bibliográficas (p. [412]-423) e índices.
1 The propositional calculus [11] --
1.1 Propositional connectives. Truth tables [11] --
1.2 Tautologies [15] --
1.3 Adequate sets of connectives [27] --
1.4 An axiom system for the propositional calculus [33] --
1.5 Independence. Many-valued logics [43] --
1.6 Other axiomatizations [45] --
2 Quantification theory [50] --
2.1 Quantifiers [50] --
2.2 First-order languages and their interpretations. Satisfiability and truth. Models [56] --
2.3 First-order theories [69] --
2.4 Properties of first-order theories [71] --
2.5 Additional metatheorems and derived rules [76] --
2.6 Rule C [81] --
2.7 Completeness theorems [84] --
2.8 First-order theories with equality [94] --
2.9 Definitions of new function letters and individual constants [103] --
2.10 Prenex normal forms [106] --
2.11 Isomorphism of interpretations. Categoricity of theories [111] --
2.12 Generalized first-order theories. Completeness and decidability [113] --
2.13 Elementary equivalence. Elementary extensions [123] --
2.14 Ultrapowers. Non-standard analysis [129] --
2.15 Semantic trees [141] --
2.16 Quantification theory allowing empty domains [147] --
3 Formal number theory [154] --
3.1 An axiom system [154] --
3.2 Number-theoretic functions and relations [170] --
3.3 Primitive recursive and recursive functions [174] --
3.4 Arithmetization. Gödel numbers [190] --
3.5 The fixed-point theorem. Gödel’s incompleteness theorem [203] --
3.6 Recursive undecidability. Church’s theorem [216] --
4 Axiomatic set theory [225] --
4.1 An axiom system [225] --
4.2 Ordinal numbers [240] --
4.3 Equinumerosity. Finite and denumerable sets [253] --
4.4 Hartogs’ theorem. Initial ordinals. Ordinal arithmetic [263] --
4.5 The axiom of choice. The axiom of regularity [275] --
4.6 Other axiomatizations of set theory [287] --
5 Computability [305] --
5.1 Algorithms. Turing machines [305] --
5.2 Diagrams [311] --
5.3 Partial recursive functions. Unsolvable problems. [317] --
5.4 The Kleene-Mostovski hierarchy. Recursively enumerable sets [333] --
5.5 Other notions of computability [345] --
5.6 Decision problems [361] --
Appendix Second-order logic [368] --
Answers to selected exercises [383] --
Bibliography [412] --
Notation [424] --
Index [427] --
MR, 99b:03002
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