Past Seminars › Seminar Series

Analytic Topology in Mathematics and Computer Science (past)

Mon, 27/02/2006
17:30 		Johan van Benthem (Amsterdam & Stanford) Analytic Topology in Mathematics and Computer Science Add to calendar L3
Knowledge, Topology and Dynamics
We will survey the topological interpretation of modal languages, with some modern features, such as the appropriate bisimulations and model comparison games. Then we move to an epistemic version of this, showing how it provides a finer set of epistemic distinctions for group behaviour, including different notions of common knowledge. We explain the background for this in an epistemic MU-calculus. Finally, if we can pull this off within the time limit, we will discuss how topological models also show up in current dynamic-epistemic systems of belief revision.    
Tue, 07/02/2006
16:00 		Henk Bruin (Surrey) Analytic Topology in Mathematics and Computer Science Add to calendar L3
To Be Announced
Mon, 16/01/2006
17:00 		Adrian Mathias (Reunion) Analytic Topology in Mathematics and Computer Science Add to calendar L3
Weak systems of set theory
Mon, 28/11/2005
17:00 		Ronnie Brown (Informatics Dept., University of Bangor) Analytic Topology in Mathematics and Computer Science Add to calendar L2
Induced constructions and their computation
Mon, 21/11/2005
17:00 		James Worrell (Computing Laboratory, Oxford) Analytic Topology in Mathematics and Computer Science Add to calendar L3
On the greatest fixed point of a set functor
Mon, 14/11/2005
17:00 		Dona Strauss (Mathematics Dept., University of Hull) Analytic Topology in Mathematics and Computer Science Add to calendar L3
The algebra of Beta S and Ramsey Theory
Mon, 14/11/2005
15:30 		Robin Knight (Oxford) Analytic Topology in Mathematics and Computer Science Add to calendar SR2
Type categories and compactifications
With a theory in a logical language is associated a {\it type category}, which is a collection of topological spaces with appropriate functions between them. If the language is countable and first-order, then the spaces are compact and metrisable. If the language is a countable fragment of $L_{\omega_1,\omega}$, and so admits some formulae of infinite length, then the spaces will be Polish, but not necessarily compact.

We describe a machine for turning theories in the more expressive $L_{\omega_1,\omega}$ into first order, by using a topological compactification. We cannot hope to achieve an exact translation; what we do instead is create a new theory whose models are the models of the old theory, together with countably many extra models which are generated by the extra points in the compactification, and are very easy to describe.

We will mention one or two applications of these ideas.
 
Mon, 31/10/2005
17:00 		Professor Boris Zilber (M.I., Oxford) Analytic Topology in Mathematics and Computer Science Add to calendar L3
Model Theory and non-commutative geometry
Mon, 16/05/2005
17:00 		Greg Meredith (Djinnisys Corporation, Seattle) Analytic Topology in Mathematics and Computer Science Add to calendar L3
Reflective calculi and namespace logic

For any corrections/updates to these listings, please contact seminars [-at-] maths [dot] ox [dot] ac [dot] uk.

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