Automorphisms with only infinite orbits on non-algebraic elements

摘要

This paper generalizes results of F. Korner 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-bar,b-bar) for which there is an ω-maximal automorphism mapping a-bar to b-bar.