Some results on lovely pairs of geometric structures
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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. | |||