Set theory and its neighbours meets the Cameleon
A oneday 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)
.
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 settheoretical
object changing its properties depending on additional settheoretic
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
ω_{1}, with pairwise finite intersection,
and chromatic number greater than ω_{6}.
The proof uses ideas of Shelah's papers
On successors of singular cardinals, Logic Colloquium '78
(Mons, 1978) (1979), pp.357380 [Sh:108] and
Antihomogeneous Partitions of a Topological Space
Scientiae Math Japonicae 59, No. 2; (special issue:e9, 449501) (2004),
pp. 203255 [Sh:668].
 Piotr
Koszmider
(São Paulo)
 Boolean algebras and projections in Banach spaces C(K) 
settheoretic 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.
Mirna Džamonja and
Charles Morgan
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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