Combinatorics and set theory, 2

The eleventh one-day conference in the in the series Set theory and its neighbours, took place on Wednesday, 3rd April 2002 at the London Mathematical Society building, De Morgan House, 57-58 Russell Square, London WC1.

The speakers at the meeting were:

• Marcin Kysiak (Polish Academy of Sciences)
  Various classes of small sets: combinatorics vs. measure and category (ps) (pdf)
  [Both at Marcin's site in Warsaw]
  Abstract: I shall talk about relations between classes of small sets in the sense of measure and/or category (like: strongly null, universally null, very meager, perfectly meager, etc.) and - that's combinatorial part - classes of small sets like s_0, l_0, m_0. In particular, I shall concentrate on some new (I hope so!) results that we have recently obtained together with Tomasz Weiss concerning Laver-null (l_0) and Miller-null (m_0) sets.
• Imre Leader (Cambridge)
  Forbidden distances in the rationals and the reals
  Abstract: We show that the reals may be partitioned into finitely many classes, each of which has `few' distances in a certain natural sense. Although the construction appears to use CH in an indispensible way, it turns out that the result remains true without CH.
• Olivier Lessman (Oxford)
  Dimension theory in homogeneous model theory
• Charles Morgan (UCL)
  Some step-ups and a few gentle stretching exercises
  Abstract: I discuss generic stepping up problems and techniques, with particular emphasis on the new notions of local connectedness functions and -M-proper forcing for arbitrary uncountable cardinals . I give some applications of these ideas to pcf theory, Lindelof spaces, and strong chains in P().
  Links to papers:
  • Local distance and connectedness functions
  • pcf structures II: the consistency of pcf structures on omega_2
  • Études in -M-proper forcing
• Greg Piper (UEA)
  Square principles on P_\kappa(\lambda)
• Rene Schipperus (University of Vienna)
  Elementary submodels in the partition calculus
  Abstract: We prove some new and old results in the partition calculus which make use of the choice of elementary submodels of (a part of) the set theoretic universe. These ideas replace the older ramification arguments and are essential to further progress. We explain all of the set theoretic notions involved.

We are very grateful to the LMS for allowing us to use De Morgan House as a venue and for their financial support for the meeting.

Return to the Set theory and its neighbours homepage for information, including slides from the talks and related preprints, about the previous meetings.

Last updated on 4th April 2002, Charles Morgan