Combinatorial Set Theory (eBook)

Front Cover 1
Combinatorial Set Theory 4
Copyright Page 5
Contents 8
Preface 6
Foreword on notation 10
Chapter 1. Almost disjoint families of sets 14
1. Almost disjoint families 14
2. Almost disjoint functions 18
3. Transversals of non-disjoint families 28
Chapter 2. Ordinary partition relations 37
1. The relations defined 37
2. The Ramification Lemma 39
3. The Stepping-up Lemma 47
4. Results for singular cardinals 49
5. The case n = 2 53
6. Results when n > 3
7. Square bracket relations 66
8. Partitions of all the finite subsets 73
Chapter 3. Set mappings 77
1. Set mappings of small order 77
2. Set mappings of large order 84
3. Set mappings of higher type 91
Chapter 4. Polarized partition relations 96
1. Partitions of K X K 96
2. Partitions of K X K+ 109
3. Larger polarized relations 118
Chapter 5. Theory of infinite graphs 123
1. The chromatic number 123
2. A colouring problem 134
3. Chromatic number of subgraphs 138
Chapter 6. Decomposition and intersection properties of families of sets 143
1. Decomposition properties 143
2. Delta-systems 154
3. Weak delta-systems 160
Chapter 7. Ordinary partition relations for ordinal numbers 166
1. Introductory remarks 166
2. Countable ordinals 170
3. Chang's Theorem for . . 181
4. Partitions of [.1] 2 186
Appendix. Cardinal and ordinal numbers 197
§ 1. Set Theory 197
§ 2. Ordinal numbers 198
§ 3. Cardinal arithmetic 202
References 209
Index of authors 214
Index of definitions 216
Index of notation 219