Logic Seminar
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Fri, 18/01/2008 14:15 |
Itai Ben Yaacov (Lyon) |
Logic Seminar  |
L3 |
| H. Jerome Keisler suggested to associate to each classical structure M a family of "random" structures consisting of random variables with values in M . Viewing the random structures as structures in continuous logic one is able to prove preservation results of various "good" model theoretic properties e.g., stability and dependence, from the original structure to its randomisation. On the other hand, simplicity is not preserved by this construction. The work discussed is mostly due to H. Jerome Keisler and myself (given enough time I might discuss some applications obtains in joint work with Alex Usvyatsov). | |||
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Fri, 25/01/2008 14:15 |
Robin Knight (Oxford) |
Logic Seminar |
L3 |
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Fri, 01/02/2008 14:15 |
TBC |
Logic Seminar |
L3 |
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Fri, 08/02/2008 14:15 |
Alex Wilkie (Manchester) |
Logic Seminar |
L3 |
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Fri, 15/02/2008 14:15 |
Ayhan Gunaydin (Oxford) |
Logic Seminar |
L3 |
| There is a well-behaving class of dense ordered abelian groups called "regularly dense ordered abelian groups". This first order property of ordered abelian groups is introduced by Robinson and Zakon as a generalization of being an archimedean ordered group. Every dense subgroup of the additive group of reals is regularly dense. In this talk we consider subgroups of the multiplicative group, S, of all complex numbers of modulus 1. Such groups are not ordered, however they have an "orientation" on them: this is a certain ternary relation on them that is invariant under multiplication. We have a natural correspondence between oriented abelian groups, on one side, and ordered abelian groups satisfying a cofinality condition with respect to a distinguished positive element 1, on the other side. This correspondence preserves model-theoretic relations like elementary equivalence. Then we shall introduce a first-order notion of "regularly dense" oriented abelian group; all infinite subgroups of S are regularly dense in their induced orientation. Finally we shall consider the model theoretic structure (R,Gamma), where R is the field of real numbers, and Gamma is dense subgroup of S satisfying the Mann property, interpreted as a subset of R^2. We shall determine the elementary theory of this structure. | |||
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Fri, 22/02/2008 14:15 |
Francois Loeser (Paris) |
Logic Seminar |
L3 |
| We shall present work in progress in collaboration with E. Hrushovski on the geometry of spaces of stably dominated types in connection with non archimedean geometry à la Berkovich | |||
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Thu, 28/02/2008 10:00 |
Piotr Kowalski (Wroclaw) |
Logic Seminar |
L3 |
| This is joint work with Assaf Hasson. We consider non-locally modular strongly minimal reducts of o-minimal expansions of reals. Under additional assumptions we show they have a Zariski structure. | |||
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Fri, 29/02/2008 14:15 |
Alexey Muranov (Lyon) |
Logic Seminar |
L3 |
Bardakov and Tolstykh have recently shown that Richard Thompson's group
 interprets the Arithmetic  with parameters. We
consider a class of infinite groups of piecewise affine permutations of
an interval which contains all the three groups of Thompson and some
classical families of finitely presented infinite simple groups. We have
interpreted the Arithmetic in all the groups of this class. In particular
we have obtained that the elementary theories of all these groups are
undecidable. Additionally, we have interpreted the Arithmetic in and
some of its generalizations without parameters.
This is a joint work with Tuna Altınel. |
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Thu, 06/03/2008 10:00 |
Nina Frohn (Freiburg) |
Logic Seminar |
SR1 |
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Fri, 07/03/2008 14:15 |
Hans Adler (Leeds) |
Logic Seminar |
L3 |
| I will explain the connection between Shelah's recent notion of strongly dependent theories and finite weight in simple theories. The connecting notion of a strong theory is new, but implicit in Shelah's book. It is related to absence of the tree property of the second kind in a similar way as supersimplicity is related to simplicity and strong dependence to NIP. | |||
