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## Elements of set theory / Herbert B. Enderton.

Editor: New York : Academic Press, c1977Descripción: xiv, 279 p. : il. ; 24 cmISBN: 0122384407Tema(s): Set theoryOtra clasificación: 03E30 (03E10)
Contenidos:
```Preface xi
List of Symbols xiii
Chapter 1 INTRODUCTION [1]
Baby Set Theory [1]
Sets—An Informal View [7]
Classes [10]
Axiomatic Method [10]
Notation [13]
Historical Notes [14]
Chapter 2 AXIOMS AND OPERATIONS [17]
Axioms [17]
Arbitrary Unions and Intersections [23]
Algebra of Sets [27]
Epilogue [33]
Review Exercises [33]
Chapter 3 RELATIONS AND FUNCTIONS [35]
Ordered Pairs [35]
Relations [39]
n-Ary Relations [41]
Functions [42]
Infinite Cartesian Products [54]
Equivalence Relations [55]
Ordering Relations [62]
Review Exercises [64]
Chapter 4 NATURAL NUMBERS [66]
Inductive Sets [67]
Peano’s Postulates [70]
Recursion on ω [73]
Arithmetic [79]
Ordering on ω [83]
Review Exercises [88]
Chapter 5 CONSTRUCTION OF THE REAL NUMBERS [90]
Integers [90]
Rational Numbers [101]
Real Numbers [111]
Summaries [121]
Two [123]
Chapter 6 CARDINAL NUMBERS AND THE AXIOM OF CHOICE [128]
Equinumerosity [128]
Finite Sets [133]
Cardinal Arithmetic [138]
Ordering Cardinal Numbers [145]
Axiom of Choice [151]
Countable Sets [159]
Arithmetic of Infinite Cardinals [162]
Continuum Hypothesis [165]
Chapter 7 ORDERINGS AND ORDINALS [167]
Partial Orderings 167 Well Orderings [172]
Replacement Axioms [179]
Epsilon-Images [182]
Isomorphisms [184]
Ordinal Numbers [187]
Debts Paid [195]
Rank [200]
Chapter 8 ORDINALS AND ORDER TYPES [209]
Transfinite Recursion Again [209]
Alephs [212]
Ordinal Operations [215]
Isomorphism Types [220]
Arithmetic of Order Types [222]
Ordinal Arithmetic [227]
Chapter 9 SPECIAL TOPICS [241]
Well-Founded Relations [241]
Natural Models [249]
Cofinality [257]
Appendix NOTATION, LOGIC, AND PROOFS [263]
Selected References for Further Study [269]
List of Axioms [271]
Index [273]```
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 En56 (Browse shelf) Available A-5152

Bibliografía: p. 269-270.

Preface xi --
List of Symbols xiii --
Chapter 1 INTRODUCTION [1] --
Baby Set Theory [1] --
Sets—An Informal View [7] --
Classes [10] --
Axiomatic Method [10] --
Notation [13] --
Historical Notes [14] --
Chapter 2 AXIOMS AND OPERATIONS [17] --
Axioms [17] --
Arbitrary Unions and Intersections [23] --
Algebra of Sets [27] --
Epilogue [33] --
Review Exercises [33] --
Chapter 3 RELATIONS AND FUNCTIONS [35] --
Ordered Pairs [35] --
Relations [39] --
n-Ary Relations [41] --
Functions [42] --
Infinite Cartesian Products [54] --
Equivalence Relations [55] --
Ordering Relations [62] --
Review Exercises [64] --
Chapter 4 NATURAL NUMBERS [66] --
Inductive Sets [67] --
Peano’s Postulates [70] --
Recursion on ω [73] --
Arithmetic [79] --
Ordering on ω [83] --
Review Exercises [88] --
Chapter 5 CONSTRUCTION OF THE REAL NUMBERS [90] --
Integers [90] --
Rational Numbers [101] --
Real Numbers [111] --
Summaries [121] --
Two [123] --
Chapter 6 CARDINAL NUMBERS AND THE AXIOM OF CHOICE [128] --
Equinumerosity [128] --
Finite Sets [133] --
Cardinal Arithmetic [138] --
Ordering Cardinal Numbers [145] --
Axiom of Choice [151] --
Countable Sets [159] --
Arithmetic of Infinite Cardinals [162] --
Continuum Hypothesis [165] --
Chapter 7 ORDERINGS AND ORDINALS [167] --
Partial Orderings 167 Well Orderings [172] --
Replacement Axioms [179] --
Epsilon-Images [182] --
Isomorphisms [184] --
Ordinal Numbers [187] --
Debts Paid [195] --
Rank [200] --
Chapter 8 ORDINALS AND ORDER TYPES [209] --
Transfinite Recursion Again [209] --
Alephs [212] --
Ordinal Operations [215] --
Isomorphism Types [220] --
Arithmetic of Order Types [222] --
Ordinal Arithmetic [227] --
Chapter 9 SPECIAL TOPICS [241] --
Well-Founded Relations [241] --
Natural Models [249] --
Cofinality [257] --
Appendix NOTATION, LOGIC, AND PROOFS [263] --
Selected References for Further Study [269] --
List of Axioms [271] --
Index [273] --

MR, 55 #12522

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