On Computable Automorphisms of the Rational Numbers

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Journal of Symbolic Logic 66 (3):1458-1470 (2001)
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Abstract

The relationship between ideals I of Turing degrees and groups of I-recursive automorphisms of the ordering on rationals is studied. We discuss the differences between such groups and the group of all automorphisms, prove that the isomorphism type of such a group completely defines the ideal I, and outline a general correspondence between principal ideals of Turing degrees and the first-order properties of such groups.

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