Abstract.
This paper generalizes results of F. Körner 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 (¯a,¯b) for which there is an ω-maximal automorphism mapping ¯a to ¯b.
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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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Duby, G. Automorphisms with only infinite orbits on non-algebraic elements. Arch. Math. Logic 42, 435–447 (2003). https://doi.org/10.1007/s00153-002-0146-y
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DOI: https://doi.org/10.1007/s00153-002-0146-y