On computable automorphisms of the rational numbers

1 September 2001

journal article
Published by Cambridge University Press (CUP) in The Journal of Symbolic Logic

Vol. 66 (3) , 1458-1470
https://doi.org/10.2307/2695118

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.

Keywords

IDEALS OF TURING
AUTOMORPHISMS
TURING DEGREES
ISOMORPHISM TYPE
GENERAL CORRESPONDENCE
PRINCIPAL IDEALS
GROUP COMPLETELY
RATIONAL NUMBERS

This publication has 3 references indexed in Scilit:

On Recovering Structures from Quotients of their Automorphism Groups
Published by Springer Nature ,1996
Permutations and implicit definability
Algebra and Logic, 1988
Ordered Permutation Groups
Published by Cambridge University Press (CUP) ,1982