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T resplendent models and the Lascar group

Tuesday 25th January 2005 - 10:00 to 12:00
INI Seminar Room 1

Daniel Lascar introduced the group having now its name as a quotient of the group Aut(M) of all automorphisms of the structure M by the normal subgroup Autf(M) of all strong automorphims of M. This construction is independent of the choice of M as far as M is a big saturated model of the complete first-order theory T and can be considered as a model-theoretic invariant of T. It is assumed although it has not been checked in detail that the same construction works for special models M whose cardinality has a big cofinality. We will carry out the construction of the Lascar group in a more general class of models, the class of |T|^{+}-resplendent models. It turns out that the proofs are more easy in this more general setting. We will present the Lascar group as a pure group and we won't discuss its topology, but the topological part adapts easily also to this context.

University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons