A one-day conference in the series Set theory and its neighbours
will take place on Wednesday,
22nd November 2006 at the Department of Mathematics, Uuiversity
College London, 25 Gordon Street, London, WC1. The first talk will be at
1pm in room 706. Subsequent talks will be in room 500. Those interested
in meeting for lunch should go to room 606 at midday.
The speakers at the meeting will be:
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.
Analytic preorders on
countable coloured total orders
Abstract: The colouring of countable total orders gives rise to
several relations of
preorders that can be studied in the framework of descriptive set theory.
Known facts will be presented and several open problems will be discussed.
Banach-Mazur game and its applications in analysis
Abstract:
It is probably well-known that the Banach-Mazur game allows us
to characterise residuality (comeagreness) in terms of the
existence of a winning strategy.
Moreover it can serve as a powerful tool when we investigate the
behaviour of typical elements of concrete spaces.
In this talk, we will give several examples of the application of the game in this direction.
MAD families with strong combinatorial properties
Abstract: Miller conjectured that under CH, there is a MAD family that is also a
σ-set and also that, again under CH, there is a MAD family
concentrated on a countable subset. Following joint work with Jorg
Brendle, I confirm these as theorems, and will present an outline proof
of the first.
The Outer Model Hypothesis
Abstract: Recent work on absoluteness of, eg, analytical statements
between the universe and its forcing extensions has concentrated on *set* generic
extensions. The current talk concerns a principle of S. Friedman that states the
universe V has many inner models so that any sentence in the language of set theory that can
possible be true in an inner model of an extension of V (whether obtained by forcing
or otherwise) is already true in an inner model of V. We report on joint work with Friedman
and Woodin in which we have investigated the strength of this principle and some of its neighbours.
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 24th October 2006, Charles Morgan
