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Problems and theorems in classical set theory

Author: Peter Komjath; Vilmos Totik
Publisher: New York ; Berlin : Springer, 2006.
Series: Problem books in mathematics.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

This is the first comprehensive collection of problems in set theory. It contains well chosen sequences of exercises. Most of the problems are challenging and require work, wit, and inspiration. The  Read more...

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Genre/Form: Textbook
Problèmes et exercices
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Peter Komjath; Vilmos Totik
ISBN: 038730293X 9780387302935 9780387362199 0387362193
OCLC Number: 68804132
Notes: Textbook.
Includes index.
Description: xii, 514 pages ; 24 cm.
Contents: Part I Problems --
1 Operations on sets 3 --
2 Countability 9 --
3 Equivalence 13 --
4 Continuum 15 --
5 Sets of reals and real functions 19 --
6 Ordered sets 23 --
7 Order types 33 --
8 Ordinals 37 --
9 Ordinal arithmetic 43 --
10 Cardinals 51 --
11 Partially ordered sets 55 --
12 Transfinite enumeration 59 --
13 Euclidean spaces 63 --
14 Zorn's lemma 65 --
15 Hamel bases 67 --
16 The continuum hypothesis 71 --
17 Ultrafilters on [omega] 75 --
18 Families of sets 79 --
19 The Banach-Tarski paradox 81 --
20 Stationary sets in [omega subscript 1] 85 --
21 Stationary sets in larger cardinals 89 --
22 Canonical functions 93 --
23 Infinite graphs 95 --
24 Partition relations 101 --
25 [Delta]-systems 107 --
26 Set mappings 109 --
27 Trees 111 --
28 The measure problem 117 --
29 Stationary sets in [lambda superscript <kappa] 123 --
30 The axiom of choice 127 --
31 Well-founded sets and the axiom of foundation 129 --
Part II Solutions --
1 Operations on sets 135 --
2 Countability 147 --
3 Equivalence 159 --
4 Continuum 163 --
5 Sets of reals and real functions 173 --
6 Ordered sets 185 --
7 Order types 213 --
8 Ordinals 223 --
9 Ordinal arithmetic 237 --
10 Cardinals 265 --
11 Partially ordered sets 275 --
12 Transfinite enumeration 285 --
13 Euclidean spaces 299 --
14 Zorn's lemma 309 --
15 Hamel bases 317 --
16 The continuum hypothesis 327 --
17 Ultrafilters on [omega] 341 --
18 Families of sets 351 --
19 The Banach-Tarski paradox 359 --
20 Stationary sets in [omega subscript 1] 369 --
21 Stationary sets in larger cardinals 377 --
22 Canonical functions 385 --
23 Infinite graphs 389 --
24 Partition relations 405 --
25 [Delta]-systems 421 --
26 Set mappings 427 --
27 Trees 433 --
28 The measure problem 453 --
29 Stationary sets in [lambda superscript <kappa] 463 --
30 The axiom of choice 471 --
31 Well-founded sets and the axiom of foundation 481.
Series Title: Problem books in mathematics.
Responsibility: Peter Komjath, Vilmos Totik.
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From the reviews:"The volume contains 1007 problems in (mostly combinatorial) set theory. As indicated by the authors, "most of classical set theory is covered, classical in the sense that Read more...

 
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