Automorphisms with only infinite orbits on non-algebraic elements |
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Authors: | Grégory Duby |
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Institution: | (1) University of Brussels, Departement of Mathematics, CP 211 Boulevard du Triomphe, 1050 Brussels, Belgium. e-mail: gduby@ulb.ac.be, BE |
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Abstract: | This paper generalizes results of F. K?rner from 4] where she established the existence of maximal automorphisms (i.e. automorphisms
moving all non-algebraic elements). An ω-maximal automorphism is an automorphism whose powers are maximal automorphisms. We
prove that any structure has an elementary extension with an ω-maximal automorphism. We also show the existence of ω-maximal
automorphisms in all countable arithmetically saturated structures. Further we describe the pairs of tuples (ˉa,ˉb) for which there is an ω-maximal automorphism mapping ˉa to ˉb.
Received: 12 December 2001 /
Published online: 10 October 2002
Supported by the ``Fonds pour la Formation à la Recherche dans l'Industrie et dans l'Agriculture'
Mathematics Subject Classification (2000): Primary: 03C50; Secondary: 03C57
Key words or phrases: Automorphism – Recursively saturated structure |
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