Logic Seminar
|
Thu, 22/01/2009 17:00 |
Sonia L'Innocente (Camerino) |
Logic Seminar  |
L3 |
| Abstract available at: http://people.maths.ox.ac.uk/~kirby/LInnocente.pdf | |||
|
Fri, 23/01/2009 16:00 |
Anand Pillay (Leeds) |
Logic Seminar |
SR2 |
| Given K a separably closed field of finite ( > 1) degree of imperfection, and semiabelian variety A over K, we study the maximal divisible subgroup A^{sharp} of A(K). We show that the {\sharp} functor does not preserve exact sequences and also give an example where A^{\sharp} does not have relative Morley rank. (Joint work with F. Benoist and E. Bouscaren) | |||
|
Thu, 29/01/2009 17:00 |
David Bew (Oxford) |
Logic Seminar |
L3 |
|
Thu, 05/02/2009 17:00 |
Olivia Caramello (Cambridge) |
Logic Seminar |
L3 |
| We present a topos-theoretic interpretation of (a categorical generalization of) Fraïssé's construction in Model Theory, with applications to countably categorical theories. The proof of our main theorem represents an instance of exploiting the interplay of syntactic, semantic and geometric ideas in the foundations of Topos Theory. | |||
|
Thu, 12/02/2009 17:00 |
Marco Ferreira (East Anglia) |
Logic Seminar |
L3 |
| In 1993 in his paper "A new strongly minimal set" Hrushovski produced a family of counter examples to a conjecture by Zilber. Each one of these counter examples carry a pregeometry. We answer a question by Hrushovski about comparing these pregeometries and their localization to finite sets. We first analyse the pregeometries arising from different variations of the construction before the collapse. Then we compare the pregeometries of the family of new strongly minimal structures obtained after the collapse. | |||
|
Thu, 19/02/2009 17:00 |
Gareth Boxall (Leeds) |
Logic Seminar |
L3 |
| Let T be a (one-sorted first order) geometric theory (so T has infinite models, T eliminates "there exist infinitely many" and algebraic closure gives a pregeometry). I shall present some results about T_P, the theory of lovely pairs of models of T as defined by Berenstein and Vassiliev following earlier work of Ben-Yaacov, Pillay and Vassiliev, of van den Dries and of Poizat. I shall present results concerning superrosiness, the independence property and imaginaries. As far as the independence property is concerned, I shall discuss the relationship with recent work of Gunaydin and Hieronymi and of Berenstein, Dolich and Onshuus. I shall also discuss an application to Belegradek and Zilber's theory of the real field with a subgroup of the unit circle. As far as imaginaries are concerned, I shall discuss an application of one of the general results to imaginaries in pairs of algebraically closed fields, adding to Pillay's work on that subject. | |||
|
Mon, 02/03/2009 15:00 |
Martin Bays (Oxford) |
Logic Seminar |
SR1 |
Let  be an elliptic curve defined over a number field  ,
and let  be a complex point. Among the
possible choices of sequences of division points of  , 
such that  and  , we can pick out those which
converge in the complex topology to the identity. We show that the
algebraic content of this effect of the complex topology is very
small, in the sense that any set of division sequences which shares
certain obvious algebraic properties with the set of those which
converge to the identity is conjugated to it by a field automorphism
of  over .
As stated, this is a result of algebra and number theory. However, in
proving it we are led ineluctably to use model theoretic techniques -
specifically the concept of "excellence" introduced by Shelah for the
analysis of  categoricity, which reduces the
question to that of proving certain unusual versions of the theorems
of Mordell-Weil and Kummer-Bashmakov. I will discuss this and other
aspects of the proof, without assuming any model- or number-theoretic
knowledge on the part of my audience. |
|||
|
Mon, 09/03/2009 15:00 |
John Wilson (Oxford) |
Logic Seminar |
SR1 |
