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On computable automorphisms of the rational numbers

Published online by Cambridge University Press:  12 March 2014

A. S. Morozov  and
J. K. Truss
A. S. Morozov
Affiliation:
Sobolev Institute of Mathematics, Novosibirsk State University, Universitetskii PZ 4, Novosibirsk 90, Russia
J. K. Truss
Affiliation:
Department of Pure Mathematics, University of Leeds, Leeds LS2 9JT, England, E-mail: j.k.truss@leeds.ac.uk
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 66 , Issue 3 , September 2001 , pp. 1458 - 1470
Copyright
Copyright © Association for Symbolic Logic 2001

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References

REFERENCES

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