Set Theory for the Working Mathematician

Front Cover
Cambridge University Press, Aug 28, 1997 - Mathematics - 236 pages
0 Reviews
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.
 

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Axiomatic set theory
3
12 The language and the basic axioms
6
Relations functions and Cartesian product
12
22 Functions and the replacement scheme axiom
16
23 Generalized union intersection and Cartesian product
19
24 Partial and linearorder relations
21
Natural numbers integers and real numbers
25
32 Integers and rational numbers
30
63 Lebesguemeasurable sets and sets with the Baire property
98
Strange real functions
104
72 Darboux functions
106
73 Additive functions and Hamel bases
111
74 Symmetrically discontinuous functions
118
When induction is too short
127
Martins axiom
129
82 Martins axiom
139

33 Real numbers
31
Fundamental tools of set theory
35
Well orderings and transfinite induction
37
42 Ordinal numbers
44
43 Definitions by transfinite induction
49
44 Zorns lemma in algebra analysis and topology
54
Cardinal numbers
61
52 Cardinal arithmetic
68
53 Cofinality
74
The power of recursive definitions
77
Subsets of ℝⁿ
79
62 Closed sets and Borel sets
89
83 Suslin hypothesis and diamond principle
154
Forcing
164
92 Forcing method and a model for CH
168
93 Model for CH and
182
94 Product lemma and Cohen model
189
95 Model for MA+CH
196
A Axioms of set theory
211
B Comments on the forcing method
215
C Notation
220
References
225
Index
229
Copyright

Other editions - View all

Common terms and phrases

References to this book

All Book Search results »

About the author (1997)

Krzysztof Ciesielski is Professor of Mathematics at West Virginia University.