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## Axiomatic set theory / by Patrick Suppes.

Editor: Princeton, New Jersey : D. van Nostrand, c1960Descripción: xii, 265 p. ; 24 cmOtra clasificación: 03E30 (03Exx)
Contenidos:
```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]
1.5 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
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] --
1.5 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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