Les beaux automorphismes

Archive for Mathematical Logic 31 (1):55-68 (1991)
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Abstract

Assume that the class of partial automorphisms of the monster model of a complete theory has the amalgamation property. The beautiful automorphisms are the automorphisms of models ofT which: 1. are strong, i.e. leave the algebraic closure (inT eq) of the empty set pointwise fixed, 2. are obtained by the Fraïsse construction using the amalgamation property that we have just mentioned. We show that all the beautiful automorphisms have the same theory (in the language ofT plus one unary function symbol for the automorphism), and we study this theory. In particular, we examine the question of the saturation of the beautiful automorphisms. We also prove that in some cases (in particular if the theory is ω-stable andG-trivial), almost all (in the sense of Baire categoricity) automorphisms of the saturated countable model are beautiful and conjugate

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Citations of this work

Generic structures and simple theories.Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95 (1-3):71-92.
Laforte, G., see Downey, R.T. Arai, Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95 (1-3):287.
Model companions of theories with an automorphism.Hirotaka Kikyo - 2000 - Journal of Symbolic Logic 65 (3):1215-1222.
The strict order property and generic automorphisms.Hirotaka Kikyo & Saharon Shelah - 2002 - Journal of Symbolic Logic 67 (1):214-216.
The definable multiplicity property and generic automorphisms.Hirotaka Kikyo & Anand Pillay - 2000 - Annals of Pure and Applied Logic 106 (1-3):263-273.

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References found in this work

Paires de structures Stables.Bruno Poizat - 1983 - Journal of Symbolic Logic 48 (2):239-249.
On the category of models of a complete theory.Daniel Lascar - 1982 - Journal of Symbolic Logic 47 (2):249-266.

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