JournalsowrVol. 2 / No. 4DOI 10.4171/owr/2005/55

Set Theory

  • Sy-David Friedman

    Universität Wien, Austria
  • Menachem Magidor

    The Hebrew University, Jerusalem, Israel
  • W. Hugh Woodin

    University of California, Berkeley, United States
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This meeting was organised by Sy-David Friedman (University of Vienna), Menachem Magidor (Hebrew University, Jerusalem) and Hugh Woodin (University of California, Berkeley). Largely due to the generous EU support for the meeting, we were able to invite an unusually large number of young researchers (at most 10 years after the beginning of doctoral studies). We consequently chose an unusual format for the meeting, in which young people were given priority in the scheduling of lectures. This turned out to be a good choice, as the quality of these lectures was extremely high, giving us an excellent opportunity to learn about the new talent that has recently come into our field.

45-minute lectures were delivered by Krueger (Vienna), Dobrinen (Vienna), Camerlo (Torino), Zoble (Toronto), Geschke (Berlin), K\"onig (Paris), Viale (Paris), Asper\'o (Barcelona), Sharon (Irvine) and Lopez-Abad (Paris). These young people presented striking new results concerning combinatorial set theory, descriptive set theory, set-theoretic analysis and forcing axioms. One of the most impressive of these new results was that of Viale, who established a connection between two important set-theoretic principles, by showing that the singular cardinal hypothesis follows from the proper forcing axiom.

Shorter lectures (20 to 30 minutes) were given by the more senior researchers. In total, lectures were held by 29 of the 59 participants. By restricting the number and length of these lectures, we were able to leave substantial time for private discussion. The 15-minute breaks between lectures were especially appreciated, giving the meeting a relaxed feeling.

The traditional Wednesday afternoon walk was a success. The Schwarzwaldkirschtorte in Wolfach was superb, and despite the rain and getting (slightly) lost in the dark, everyone made it safely back to the institute in time for dinner.