Axiomatic set theory / by Patrick Suppes.
Series The university series in undergraduate mathematicsEditor: Princeton, New Jersey : D. van Nostrand, c1960Descripción: xii, 265 p. ; 24 cmOtra clasificación: 03E30 (03Exx)1. INTRODUCTION [1] 1.1 Set Theory and the Foundations of Mathematics [1] 1.2 Logic and Notation [3] 1.3 Axiom Schema of Abstraction and Russell's Paradox [5] 1.4 More Paradoxes [8] 1.5 Preview of Axioms [12] 2. GENERAL DEVELOPMENTS [14] 2.1 Preliminaries: Formulas and Definitions [14] 2.2 Axioms of Extensionality and Separation [19] 2.3 Intersection, Union, and Difference of Sets [24] 2.4 Pairing Axiom and Ordered Pairs [30] 2.5 Definition by Abstraction [33] 2.6 Sum Axiom and Families of Sets [37] 2.7 Power Set Axiom [46] 2.8 Cartesian Product of Sets [49] 2.9 Axiom of Regularity [53] 2.10 Summary of Axioms [56] 3. RELATIONS AND FUNCTIONS [57] 3.1 Operations on Binary Relations [57] 3.2 Ordering Relations [68] 3.3 Equivalence Relations and Partitions [80] 3.4 Functions [86] 4. EQUIPOLLENCE, FINITE SETS, AND CARDINAL NUMBERS [91] 4.1 Equipollence [91] 4.2 Finite Sets [98] 4.3 Cardinal Numbers [109] 4.4 Finite Cardinals [121] 5. FINITE ORDINALS AND DENUMERABLE SETS [127] 5.1 Definition and General Properties of Ordinals [127] 5.2 Finite Ordinals and Recursive Definitions [135] 5.3 Denumerable Sets [150] 6. RATIONAL NUMBERS AND REAL NUMBERS [159] 6.1 Introduction [159] 6.2 Fractions [161] 6.3 Non-negative Rational Numbers [166] 6.4 Rational Numbers [170] 6.5 Cauchy Sequences of Rational Numbers [174] 6.6 Real Numbers [181] 6.7 Sets of the Power of the Continuum [189] 7. TRANSFINITE INDUCTION AND ORDINAL ARITHMETIC [195] 7.1 Transfinite Induction and Definition by Transfinite Recursion [195] 7.2 Elements of Ordinal Arithmetic [205] 7.3 Cardinal Numbers Again and Alephs [224] 7.4 Well-Ordered Sets [230] 7.5 Revised Summary of Axioms [237] 8. THE AXIOM OF CHOICE [239] 8.1 Some Applications of the Axiom of Choice [239] 8.2 Equivalents of the Axiom of Choice [243] 8.3 Axioms Which Imply the Axiom of Choice [251] References [253] Glossary of Symbols [257] Author Index [259] Subject Index [261]
| Item type | Home library | Call number | Materials specified | Status | Date due | Barcode | Course reserves |
|---|---|---|---|---|---|---|---|
Libros
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Instituto de Matemática, CONICET-UNS | 03 Su959 (Browse shelf) | Available | A-886 |
Incluye referencias bibliográficas (p. 253-256) e índices.
1. INTRODUCTION [1] --
1.1 Set Theory and the Foundations of Mathematics [1] --
1.2 Logic and Notation [3] --
1.3 Axiom Schema of Abstraction and Russell's Paradox [5] --
1.4 More Paradoxes [8] --
1.5 Preview of Axioms [12] --
2. GENERAL DEVELOPMENTS [14] --
2.1 Preliminaries: Formulas and Definitions [14] --
2.2 Axioms of Extensionality and Separation [19] --
2.3 Intersection, Union, and Difference of Sets [24] --
2.4 Pairing Axiom and Ordered Pairs [30] --
2.5 Definition by Abstraction [33] --
2.6 Sum Axiom and Families of Sets [37] --
2.7 Power Set Axiom [46] --
2.8 Cartesian Product of Sets [49] --
2.9 Axiom of Regularity [53] --
2.10 Summary of Axioms [56] --
3. RELATIONS AND FUNCTIONS [57] --
3.1 Operations on Binary Relations [57] --
3.2 Ordering Relations [68] --
3.3 Equivalence Relations and Partitions [80] --
3.4 Functions [86] --
4. EQUIPOLLENCE, FINITE SETS, AND CARDINAL NUMBERS [91] --
4.1 Equipollence [91] --
4.2 Finite Sets [98] --
4.3 Cardinal Numbers [109] --
4.4 Finite Cardinals [121] --
5. FINITE ORDINALS AND DENUMERABLE SETS [127] --
5.1 Definition and General Properties of Ordinals [127] --
5.2 Finite Ordinals and Recursive Definitions [135] --
5.3 Denumerable Sets [150] --
6. RATIONAL NUMBERS AND REAL NUMBERS [159] --
6.1 Introduction [159] --
6.2 Fractions [161] --
6.3 Non-negative Rational Numbers [166] --
6.4 Rational Numbers [170] --
6.5 Cauchy Sequences of Rational Numbers [174] --
6.6 Real Numbers [181] --
6.7 Sets of the Power of the Continuum [189] --
7. TRANSFINITE INDUCTION AND ORDINAL ARITHMETIC [195] --
7.1 Transfinite Induction and Definition by Transfinite Recursion [195] --
7.2 Elements of Ordinal Arithmetic [205] --
7.3 Cardinal Numbers Again and Alephs [224] --
7.4 Well-Ordered Sets [230] --
7.5 Revised Summary of Axioms [237] --
8. THE AXIOM OF CHOICE [239] --
8.1 Some Applications of the Axiom of Choice [239] --
8.2 Equivalents of the Axiom of Choice [243] --
8.3 Axioms Which Imply the Axiom of Choice [251] --
References [253] --
Glossary of Symbols [257] --
Author Index [259] --
Subject Index [261] --
MR, 22 #5576
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