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An Isaac Newton Institute Programme

Model Theory and Applications to Algebra and Analysis

|T|^+-resplendent models and the Lascar group

25th January 2005

Author: Enrique Casanovas (Barcelona)

Abstract

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.