Journal of Symbolic Logic

On Computable Automorphisms of the Rational Numbers

A. S. Morozov and J. K. Truss

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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.

Article information

Source
J. Symbolic Logic, Volume 66, Issue 3 (2001), 1458-1470.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183746571

Mathematical Reviews number (MathSciNet)
MR1856753

Zentralblatt MATH identifier
0990.03034

JSTOR
links.jstor.org

Citation

Morozov, A. S.; Truss, J. K. On Computable Automorphisms of the Rational Numbers. J. Symbolic Logic 66 (2001), no. 3, 1458--1470. https://projecteuclid.org/euclid.jsl/1183746571


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