A Set Theory Workbook

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Springer Science & Business Media, Dec 18, 1997 - Mathematics - 154 pages
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This book is a companion to A general topology workbook published by Birkhiiuser last year. In an ideal world the order of publication would have been reversed, for the notation and some of the results of the present book are used in the topology book and on the other hand (the reader may be assured) no topology is used here. Both books share the word Workbook in their titles. They are based on the principle that for at least some branches of mathematics a good way for a student to learn is to be presented with a clear statement of the definitions of the terms with which the subject is concerned and then to be faced with a collection of problems involving the terms just defined. In adopting this approach with my Dundee students of set theory and general topology I found it best not to differentiate too precisely between simple illustrative examples, easy exercises and results which in conventional textbooks would be labelled as Theorems.
 

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Contents

FIRST AXIOMS OF THE THEORY NBG
7
RELATIONS
13
FUNCTIONAL RELATIONS AND MAPPINGS
19
FAMILIES OF SETS
29
EQUIVALENCE RELATIONS
35
ORDER RELATIONS
41
WELLORDERING
47
ORDINALS
51
ANSWERS TO CHAPTER 2
81
ANSWERS TO CHAPTER 3
85
ANSWERS TO CHAPTER 4
95
ANSWERS TO CHAPTER 5
101
ANSWERS TO CHAPTER 6
107
ANSWERS TO CHAPTER 7
111
ANSWERS TO CHAPTER 8
115
ANSWERS TO CHAPTER 9
121

NATURAL NUMBERS
55
EQUIVALENTS OF THE AXIOM OF CHOICE
59
INFINITE SETS
63
CARDINALS
65
CARDINAL AND ORDINAL ARITHMETIC
69
ANSWERS
75
ANSWERS TO CHAPTER 1
77
ANSWERS TO CHAPTER 10
125
ANSWERS TO CHAPTER 11
131
ANSWERS TO CHAPTER 12
135
ANSWERS TO CHAPTER 13
139
INDEX
151
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Page 3 - R denote the set of all sets which are not members of themselves.
Page 4 - ... p is equivalent to q" or p if and only if q...
Page 4 - A sentence is closed if it contains no free variables; otherwise it is open.

About the author (1997)

Adamson-The University of Dundee, Scotland

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