Logic Seminar
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Thu, 21/01/2010 17:00 |
Gareth Jones (Manchester) |
Logic Seminar  |
L3 |
| I'll give a brief survey of what is known about the density of rational points on definable sets in o-minimal expansions of the real field, then discuss improving these results in certain cases. | |||
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Thu, 28/01/2010 17:00 |
Jeroen Demeyer (Gwent) |
Logic Seminar |
L3 |
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Thu, 28/01/2010 17:00 |
Jeroen Demeyer (Ghent) |
Logic Seminar |
L3 |
| Let R be a number field (or a recursive subring of anumber field) and consider the polynomial ring R[T].We show that the set of polynomials with integercoefficients is diophantine (existentially definable) over R[T].Applying a result by Denef, this implies that everyrecursively enumerable subset of R[T]^k is diophantine over R[T]. | |||
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Thu, 04/02/2010 17:00 |
Philip Scowcroft (Wesleyan/Oxford) |
Logic Seminar |
L3 |
| I will discuss the special properties of dimension groups obtained by model-theoretic forcing | |||
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Thu, 11/02/2010 17:00 |
Alexandre Borovik (Manchester) |
Logic Seminar |
L3 |
| The talks will discuss relations between two major conjectures in the theory of groups of finite Morley rank, a modern chapter of model theoretic algebra. One conjecture, the famous the Cherlin-Zilber Algebraicity Conjecture formulated in 1970-s states that infinite simple groups of finite Morley rank are isomorphic to simple algebraic groups over algebraically closed fields. The other conjecture, due to Hrushovski and more recent, states that a generic automorphism of a simple group of finite Morley rank has pseudofinite group of fixed points. Hrushovski showed that the Cherlin-Zilber Conjecture implies his conjecture. Proving Hrushovski's Conjecture and reversing the implication would provide a new efficient approach to proof of Cherlin-Zilber Conjecture. Meanwhile, the machinery that is already available for the work at pseudofinite/finite Morley rank interface already yields an interesting result: an alternative proof of the Larsen-Pink Theorem (the latter says, roughly speaking, that "large" finite simple groups of matrices are Chevalley groups over finite fields). | |||
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Thu, 18/02/2010 17:00 |
Nicolai Vorobjov (Bath) |
Logic Seminar |
L3 |
| We study upper bounds on topological complexity of sets definable in o-minimal structures over the reals. We suggest a new construction for approximating a large class of definable sets, including the sets defined by arbitrary Boolean combinations of equations and inequalities, by compact sets. Those compact sets bound from above the homotopies and homologies of the approximated sets. The construction is applicable to images under definable maps. Based on this construction we refine the previously known upper bounds on Betti numbers of semialgebraic and semi-Pfaffian sets defined by quantifier-free formulae, and prove similar new upper bounds, individual for different Betti numbers, for their images under arbitrary continuous definable maps. Joint work with A. Gabrielov. | |||
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Thu, 25/02/2010 17:00 |
Jonathan Pila (Bristol and Oxford) |
Logic Seminar |
L3 |
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Thu, 04/03/2010 11:00 |
Andreas Doering (Oxford) |
Logic Seminar |
SR2 |
| Standard quantum logic, as intitiated by Birkhoff and von Neumann, suffers from severe problems which relate quite directly to interpretational issues in the foundations of quantum theory. In this talk, I will present some aspects of the so-called topos approach to quantum theory, as initiated by Isham and Butterfield, which aims at a mathematical reformulation of quantum theory and provides a new, well-behaved form of quantum logic that is based upon the internal logic of a certain (pre)sheaf topos. | |||
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Thu, 11/03/2010 16:30 |
Charles Parsons (Harvard) |
Logic Seminar |
Ryle Room (10 Merton Street) |
