Set Theory for the Working Mathematician

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Cambridge University Press, Aug 28, 1997 - Mathematics - 236 pages
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This text presents methods of modern set theory as tools that can be usefully applied to other areas of mathematics. The author describes numerous applications in abstract geometry and real analysis and, in some cases, in topology and algebra. The book begins with a tour of the basics of set theory, culminating in a proof of Zorn's Lemma and a discussion of some of its applications. The author then develops the notions of transfinite induction and descriptive set theory, with applications to the theory of real functions. The final part of the book presents the tools of "modern" set theory: Martin's Axiom, the Diamond Principle, and elements of forcing. Written primarily as a text for beginning graduate or advanced level undergraduate students, this book should also interest researchers wanting to learn more about set theoretical techniques applicable to their fields.
  

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Contents

III
3
IV
6
V
12
VI
16
VII
19
VIII
21
IX
25
X
30
XXIII
98
XXIV
104
XXV
106
XXVI
111
XXVII
118
XXVIII
127
XXIX
129
XXX
139

XI
31
XII
35
XIII
37
XIV
44
XV
49
XVI
54
XVII
61
XVIII
68
XIX
74
XX
77
XXI
79
XXII
89
XXXI
154
XXXII
164
XXXIV
168
XXXV
182
XXXVI
189
XXXVII
196
XXXVIII
211
XXXIX
215
XL
220
XLI
225
XLII
229
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About the author (1997)

Krzysztof Ciesielski is Professor of Mathematics at West Virginia University.