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## Set theory and logic / by Robert R. Stoll.

Editor: San Francisco : W. H. Freeman, c1961, c1963Descripción: xiv, 474 p. ; 24 cmOtro título: Introduction to set theory and logic [Título de cubierta]Otra clasificación: 03-01
Contenidos:
```Chapter 1 SETS AND RELATIONS [1]
1. Cantor’s Concept of a Set [2]
2. The Basis of Intuitive Set Theory [4]
3. Inclusion [9]
4. Operations for Sets [12]
5. The Algebra of Sets [16]
6. Relations [23]
7. Equivalence Relations [29]
8. Functions [34]
9. Composition and Inversion for Functions [38]
10. Operations for Collections of Sets [43]
11. Ordering Relations [48]
Chapter 2 THE NATURAL NUMBER SEQUENCE
AND ITS GENERALIZATIONS [56]
1. The Natural Number Sequence [57]
2. Proof and Definition by Induction [70]
3. Cardinal Numbers [79]
4. Countable Sets [87]
5. Cardinal Arithmetic [95]
6. Order Types [98]
7. Well-ordered Sets and Ordinal Numbers [102]
8. The Axiom of Choice, the Well-ordering Theorem, and Zorn’s Lemma [111]
9. Further Properties of Cardinal Numbers [118]
10. Some Theorems Equivalent to the Axiom of Choice [124]
11. The Paradoxes of Intuitive Set Theory [126]
Chapter 3 THE EXTENSION OF THE NATURAL NUMBERS TO THE REAL NUMBERS [130]
1. The System of Natural Numbers [130]
2. Differences [132]
3. Integers [134]
4. Rational Numbers [137]
5. Cauchy Sequences of Rational Numbers [142]
6. Real Numbers [149]
7. Further Properties of the Real Number System [154]
Chapter 4 LOGIC [160]
1. The Statement Calculus. Sentential Connectives [160]
2. The Statement Calculus. Truth Tables [164]
3. The Statement Calculus. Validity [169]
4. The Statement Calculus. Consequence [179]
5. The Statement Calculus. Applications [187]
6. The Predicate Calculus. Symbolizing
Everyday Language [192]
7. The Predicate Calculus. A Formulation [200]
8. The Predicate Calculus. Validity [205]
9. The Predicate Calculus. Consequence [215]
Chapter 5 INFORMAL AXIOMATIC MATHEMATICS [221]
1. The Concept of an Axiomatic Theory [221]
2. Informal Theories [227]
3. Definitions of Axiomatic Theories by
Set-theoretical Predicates [233]
4. Further Features of Informal Theories [236]
Chapter 6 BOOLEAN ALGEBRAS [248]
1. A Definition of a Boolean Algebra [248]
2. Some Basic Properties of a Boolean Algebra [250]
3. Another Formulation of the Theory [254]
4. Congruence Relations for a Boolean Algebra [259]
5. Representations of Boolean Algebras [267]
6. Statement Calculi as Boolean Algebras [273]
7. Free Boolean Algebras [274]
8. Applications of the Theory of Boolean Algebras to Statement Calculi [278]
9. Further Interconnections between Boolean Algebras and Statement Calculi [282]
Chapter 7 INFORMAL AXIOMATIC SET THEORY [289]
1. The Axioms of Extension and Set Formation [289]
1. The Axiom of Pairing [292]
3. The Axioms of Union and Power Set [294]
4. The Axiom of Infinity [297]
5. The Axiom of Choice [302]
6. The Axiom Schemas of Replacement and Restriction [302]
7. Ordinal Numbers [306]
8. Ordinal Arithmetic [312]
9. Cardinal Numbers and Their Arithmetic [316]
10. The von Neumann-Bernays-Gödel Theory of Sets [318]
Chapter 8 SEVERAL ALGEBRAIC THEORIES [321]
1. Features of Algebraic Theories [322]
2. Definition of a Semigroup [324]
3. Definition of a Group [329]
4. Subgroups [333]
5. Coset Decompositions and Congruence Relations for Groups [339]
6. Rings, Integral Domains, and Fields [346]
7. Subrings and Difference Rings [351]
8. A Characterization of the System of Integers [357]
9. A Characterization of the System of Rational Numbers [361]
10. A Characterization of the Real Number System [367]
FIRST-ORDER THEORIES [373]
1. Formal Axiomatic Theories [373]
2. The Statement Calculus as a Formal Axiomatic Theory [375]
3. Predicate Calculi of First Order as Formal Axiomatic Theories [387]
4. First-order Axiomatic Theories [394]
5. Metamathematics [401]
6. Consistency and Satisfiability of Sets of Formulas [409]
7. Consistency, Completeness, and Categoricity of First-order Theories [417]
8. Turing Machines and Recursive Functions [426]
9. Some Undecidable and Some Decidable Theories [436]
10. Gödel’s Theorems [446]
11. Some Further Remarks about Set Theory [452]
References [457]
Symbols and Notation [465]
Author Index [467]
Subject Index [469]
```
Item type Home library Shelving location Call number Materials specified Status Date due Barcode Course reserves
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Libros ordenados por tema 03 St875 (Browse shelf) Available A-1417

Chapter 1 SETS AND RELATIONS [1] --
1. Cantor’s Concept of a Set [2] --
2. The Basis of Intuitive Set Theory [4] --
3. Inclusion [9] --
4. Operations for Sets [12] --
5. The Algebra of Sets [16] --
6. Relations [23] --
7. Equivalence Relations [29] --
8. Functions [34] --
9. Composition and Inversion for Functions [38] --
10. Operations for Collections of Sets [43] --
11. Ordering Relations [48] --
Chapter 2 THE NATURAL NUMBER SEQUENCE --
AND ITS GENERALIZATIONS [56] --
1. The Natural Number Sequence [57] --
2. Proof and Definition by Induction [70] --
3. Cardinal Numbers [79] --
4. Countable Sets [87] --
5. Cardinal Arithmetic [95] --
6. Order Types [98] --
7. Well-ordered Sets and Ordinal Numbers [102] --
8. The Axiom of Choice, the Well-ordering Theorem, and Zorn’s Lemma [111] --
9. Further Properties of Cardinal Numbers [118] --
10. Some Theorems Equivalent to the Axiom of Choice [124] --
11. The Paradoxes of Intuitive Set Theory [126] --
Chapter 3 THE EXTENSION OF THE NATURAL NUMBERS TO THE REAL NUMBERS [130] --
1. The System of Natural Numbers [130] --
2. Differences [132] --
3. Integers [134] --
4. Rational Numbers [137] --
5. Cauchy Sequences of Rational Numbers [142] --
6. Real Numbers [149] --
7. Further Properties of the Real Number System [154] --
Chapter 4 LOGIC [160] --
1. The Statement Calculus. Sentential Connectives [160] --
2. The Statement Calculus. Truth Tables [164] --
3. The Statement Calculus. Validity [169] --
4. The Statement Calculus. Consequence [179] --
5. The Statement Calculus. Applications [187] --
6. The Predicate Calculus. Symbolizing --
Everyday Language [192] --
7. The Predicate Calculus. A Formulation [200] --
8. The Predicate Calculus. Validity [205] --
9. The Predicate Calculus. Consequence [215] --
Chapter 5 INFORMAL AXIOMATIC MATHEMATICS [221] --
1. The Concept of an Axiomatic Theory [221] --
2. Informal Theories [227] --
3. Definitions of Axiomatic Theories by --
Set-theoretical Predicates [233] --
4. Further Features of Informal Theories [236] --
Chapter 6 BOOLEAN ALGEBRAS [248] --
1. A Definition of a Boolean Algebra [248] --
2. Some Basic Properties of a Boolean Algebra [250] --
3. Another Formulation of the Theory [254] --
4. Congruence Relations for a Boolean Algebra [259] --
5. Representations of Boolean Algebras [267] --
6. Statement Calculi as Boolean Algebras [273] --
7. Free Boolean Algebras [274] --
8. Applications of the Theory of Boolean Algebras to Statement Calculi [278] --
9. Further Interconnections between Boolean Algebras and Statement Calculi [282] --
Chapter 7 INFORMAL AXIOMATIC SET THEORY [289] --
1. The Axioms of Extension and Set Formation [289] --
1. The Axiom of Pairing [292] --
3. The Axioms of Union and Power Set [294] --
4. The Axiom of Infinity [297] --
5. The Axiom of Choice [302] --
6. The Axiom Schemas of Replacement and Restriction [302] --
7. Ordinal Numbers [306] --
8. Ordinal Arithmetic [312] --
9. Cardinal Numbers and Their Arithmetic [316] --
10. The von Neumann-Bernays-Gödel Theory of Sets [318] --
Chapter 8 SEVERAL ALGEBRAIC THEORIES [321] --
1. Features of Algebraic Theories [322] --
2. Definition of a Semigroup [324] --
3. Definition of a Group [329] --
4. Subgroups [333] --
5. Coset Decompositions and Congruence Relations for Groups [339] --
6. Rings, Integral Domains, and Fields [346] --
7. Subrings and Difference Rings [351] --
8. A Characterization of the System of Integers [357] --
9. A Characterization of the System of Rational Numbers [361] --
10. A Characterization of the Real Number System [367] --
FIRST-ORDER THEORIES [373] --
1. Formal Axiomatic Theories [373] --
2. The Statement Calculus as a Formal Axiomatic Theory [375] --
3. Predicate Calculi of First Order as Formal Axiomatic Theories [387] --
4. First-order Axiomatic Theories [394] --
5. Metamathematics [401] --
6. Consistency and Satisfiability of Sets of Formulas [409] --
7. Consistency, Completeness, and Categoricity of First-order Theories [417] --
8. Turing Machines and Recursive Functions [426] --
9. Some Undecidable and Some Decidable Theories [436] --
10. Gödel’s Theorems [446] --
11. Some Further Remarks about Set Theory [452] --
References [457] --
Symbols and Notation [465] --
Author Index [467] --
Subject Index [469] --

MR, 30 #11

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