The Boise Extravaganza in Set Theory (BEST) started in 1992 as a small,
locally funded conference dedicated to Set Theory and its Applications. A number
of years after its inception BEST started being funded by the National Science
Foundation. Without this funding it would not have been possible to maintain the
The conference remained relatively small with many opportunities for its par-
ticipants to meet informally. We like to think that during these years BEST has
made it possible for the numerous set theorists who have participated in it to ab-
sorb, besides the new developments featured in the conference talks, also part of the
folklore and traditions of the field of set theory and its relatives. An explicit effort
was made to bring together role models from various career stages as well as the
new generation to support some notion of continuity in the field. A list of these in-
vited speakers follows this preface. The interested reader can find more information
about the past BEST conferences at∼best.
This volume has a similar purpose. In it the reader will find valuable papers
ranging from surveys that make available knowledge that has been around for sev-
eral decades as unpublished lore, to hybrid survey-research papers, to pure research
papers. Readers can be assured of the authority of each paper since each has been
carefully refereed. The reader will also find that the subjects treated in these pa-
pers range over several of the historically strongly represented areas of set theory
and its relatives. Rather than expound the virtues of each paper individually here,
we invite the reader to learn from the authors.
Bringing to publication such a collection of papers is not possible without the
generous dedication of authors and referees and the services of a publisher. We
would like to thank all authors and referees for their selfless contributions to this
volume. And we particularly would like to thank the publisher, Contemporary
Mathematics, and Christine Thivierge, for the guidance they provided during this
Liljana Babinkostova,
Andr´ es E. Caicedo,
Stefan Geschke
Marion Scheepers.
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