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  1. Model Companions of Theories with an Automorphism.Hirotaka Kikyo - 2000 - Journal of Symbolic Logic 65 (3):1215-1222.
    For a theory T in L, T σ is the theory of the models of T with an automorphism σ. If T is an unstable model complete theory without the independence property, then T σ has no model companion. If T is an unstable model complete theory and T σ has the amalgamation property, then T σ has no model companion. If T is model complete and has the fcp, then T σ has no model completion.
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  • The Strict Order Property and Generic Automorphisms.Hirotaka Kikyo & Saharon Shelah - 2002 - Journal of Symbolic Logic 67 (1):214-216.
    If T is a model complete theory with the strict order property, then the theory of the models of T with an automorphism has no model companion.
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  • The Definable Multiplicity Property and Generic Automorphisms.Hirotaka Kikyo & Anand Pillay - 2000 - Annals of Pure and Applied Logic 106 (1-3):263-273.
    Let T be a strongly minimal theory with quantifier elimination. We show that the class of existentially closed models of T{“σ is an automorphism”} is an elementary class if and only if T has the definable multiplicity property, as long as T is a finite cover of a strongly minimal theory which does have the definable multiplicity property. We obtain cleaner results working with several automorphisms, and prove: the class of existentially closed models of T{“σi is an automorphism”: i=1,2} is (...)
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  • Generic Structures and Simple Theories.Z. Chatzidakis & A. Pillay - 1998 - Annals of Pure and Applied Logic 95 (1-3):71-92.
    We study structures equipped with generic predicates and/or automorphisms, and show that in many cases we obtain simple theories. We also show that a bounded PAC field is simple. 1998 Published by Elsevier Science B.V. All rights reserved.
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  • Les Beaux Automorphismes.Daniel Lascar - 1991 - Archive for Mathematical Logic 31 (1):55-68.
    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 (...)
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