The nineth oneday
conference in the in the series Set theory and its neighbours,
took place on
Wednesday, 25th April 2001 at
the London
Mathematical Society building, De Morgan House, 5758 Russell
Square, London WC1.
The speakers at the meeting were:

Russell Barker (Oxford),
Robinsontype relations and the
relationship between the ksize and cardinality of finite structures
In this talk I will introduce the notions of L^k, the restriction of first
order logic to kvariables, the ksize of a model and, two conjectures
proposed by Anuj Dawar. Then I shall define define a special kind of
relation which I shall call a Robinsontype relation and prove some
results about these relations. I shall go on to give a translation between
these relations and the set of L^3 theories and then use the earlier
results to disprove Dawar's second conjecture.

Mirna Džamonja
(UEA),
Combinatorial principles that follow from GCHlike cardinal arithmetic
assumptions
Abstract:
We discuss various results showing that at certain cardinals diamondlike
principles follow just from local GCHlike assumptions on cardinal
arithmetic.

Peter Koepke (Bonn),
A new finestructure theory for constructible inner models:
Abstract: We present a natural hierarchy for Godel's model L of
constructible sets. The new hierarchy is immediately adequate for
finestructural arguments. This will be demonstrated by a proof of
Jensen's Covering Theorem for L. Further applications will be
discussed.

Justin Moore (UEA),
What makes the continuum $\aleph_2$?
Abstract: I will discuss some of the past, present, and
future of the
statement "The continuum has size $\aleph_2$."

Iain Stewart (Leicester), Finite model theory, computational
complexity and program schemes
Abstract: Finite model theory has strong connections with a number of topics
within computer science. For example, assuming that every finite structure
comes equipped with an ordering of its elements enables one to logically
capture most mainstream complexity classes. However, one cannot always
assume that one has access to an ordering of the elements of some finite
structure: in database theory, for example, such orderings are almost always
not available. In this talk I shall outline the concept of a program scheme,
which is essentially a model for computing on arbitrary (not necessarily
ordered) finite structures that sits somewhere between a Turing machine and
a logical formula yet remains amenable to logical manipulation. I will show
that many classes of program schemes have alternative formulations as
previouslystudied logics from finite model theory but that there are
natural classes of program schemes giving rise to "new" logics with
interesting properties.
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.
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 29th August 2001