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During the summer of 1999, Andras Hajnal was diagnosed with lung cancer. In order to provide Andras with a pleasant weekend in the midst of is treatment, it was decided that and international conference on Set Theory should be organized in his honour. As scheduled date of the conference drew nearer, there was some concern that it might coincide with Andras's surgery. But, in the end, the timing could not have been better. A week before, it finally became clear that Andras's treatment had been successful and the conference turned into a celebration of his complete recovery. (Only one of the participants was heard to complain that if he had known how healthy Andras was, he would not have come.)
There can have been few conferences which were easier to organize. Because fo the respect and deep affection which everybody in Set Theory has for Andras, there was no difficulty in putting together an outstanding program, which included many of the leaders in the field. The only difficulty concerned the name of the conference. Of course, there could be no question that Andras fully deserved a conference in his honour. Everybody is aware of his fundamental work in combinatorial set theory, cardinal arithmetic, set theoretic topology, as well as in finite and infinite combinatorics. However, especially before it became clear that he would fully recover his health, it seemed a little indelicate to officially refer to it as the Hajnal Conference. (Somebody made the slightly bizarre suggestion that it should be advertised as a conference to celebrate Andras's 68th birthday.) But now two years have passed and we can finally openly admit that the conference was held in honour of András and dedicate these Proceedings to him on the occasion of his 70th birthday.
The conference was supported by Rutgers University through the generosity of Mark Gordon and by NSF funds administered by MAMLS. All of the papers in this volume were refereed. I would like to thank the referees for their helpful and timely reports. Thanks are also due to Martin Goldstern for his patient guidance around some of the mysteries of TeX. Finally, I would like to thank Shirley Hill and Gil Poulin for their invaluable help in producing this book.
Foreword ix
Preface xi
Containment does not imply Borel reducibility
S. Adams 1
Hajnal's contributions to combinatorial set theory
and the partition calculus
J. E. Baumgartner 25
Multicolored graphs on countable ordinals of finite
exponent
C. Darby and J. A. Larson 31
On D-spaces and discrete families of sets
M. Dzamonja 45
Analytic Hausdorff gaps
I. Farah 65
Stationary sets, Chang?s conjecture and partition
theory
M. D. Foreman 73
A consistent example of a hereditarily c-Lindelof
first countable space of size > c
I. Juhasz, L. Soukup, and Z. Szentmiklsssy 95
Subgraph chromatic number
P. Komjath 99
Superatomic Boolean algebras: Maximal rigidity
S. Shelah 107
Some applications of superrigidity to Borel
equivalence relations
S. Thomas 129
Localized reflection and fragments of PFA
S. Todorcevic 135
The basis problem for CCC posets
B. Velickovic 149
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