Set theory and its neighbours meets the Cameleon

A one-day conference in the series Set theory and its neighbours but under the auspices of Cameleon, took place on Wednesday, 15th March 2006 at the Department of Mathematics, Uuniversity College London, 25 Gordon Street, London, WC1.

The speakers at the meeting were:

• Taras Banakh (Lviv/Kielce)
  • Theory of semifilters
  . A semifilter is a family of infinite subsets of ω, closed under taking almost supersets. The set of semifilters forms an compact Lawson lattice having an additional involutive operation. The quotient of this lattice by the coherence relation (so called Coherence Lattice) is a very interesting set-theoretical object changing its properties depending on additional set-theoretic axioms. In fact, semifilters came from Selection Principles and have many application in that field. Talk Notes (pdf)
• Mirna Džamonja (East Anglia)
  • Recognising Boolean algebras that carry a measure with given properties
    
  Abstract: A strictly positive measure on a Boolean algebra is a finitely or countably additive (depending on the context) measure which assigns positive value to every nonzero element of the algebra. Recognising by means of a combinatorial criterion which algebras carry such a measure has been a topic of continuous interest at least since von Neumann asked in 1937 in The Scottish Book whether every ccc weakly distributive Boolean algebra is a measure algebra. We shall discuss finitely additive strictly positive measures with the motivation of recognising when a Boolean algebra carries such a measure with some additional properties, such as separability or homogeneity.
               Mirna Džamonja and Grzegorz Plebanek, Strictly Positive Measures on Boolean Algebras (ps)
• Peter Komjáth (Eötvös)
  • Almost disjoint set systems
  Abstract: It is consistent, from a supercompact cardinal, that there is a system of sets, each of cardinality ω₁, with pairwise finite intersection, and chromatic number greater than ω₆. The proof uses ideas of Shelah's papers On successors of singular cardinals, Logic Colloquium '78 (Mons, 1978) (1979), pp.357-380 [Sh:108] and Anti--homogeneous Partitions of a Topological Space Scientiae Math Japonicae 59, No. 2; (special issue:e9, 449-501) (2004), pp. 203-255 [Sh:668].
• Piotr Koszmider (São Paulo)
  • Boolean algebras and projections in Banach spaces C(K) - set-theoretic aspects.
  Abstract: We will discuss failed and successful attempts at obtaining insights on projections in Banach spaces of the form C(K) from infinitary combinatorial structure of Boolean algebras.
• Matteo Viale (Paris).
  • Forcing axioms and cardinal arithmetic.
  Abstract: We give a brief presentation of forcing axioms and of their effect on cardinal arithmetic with a particular emphasis on my recent result that the Proper Forcing Axiom implies the Singular Cardinal Hypothesis. Talk Slides (pdf)

We aim to keep the meetings fairly relaxed, allowing plenty of opportunity for informal discussion. We welcome and encourage anyone to participate. Please do tell anyone about the meeting who you think may be interested in it. We are happy for you to email us to let us know if you intend to come, but you are also very welcome simply to turn up on the day if you make a late decision. And let us know if you would like to speak or have ideas for speakers at future meetings.

There is no registration fee for the meeting. We may have some limited funds to subsidise the travel expenses of graduate students who would like to attend. Please contact us for details.

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 16th March 2006, Charles Morgan