Geodesic
Definable sets in automorphism groups of rational order
Algebra i logika, Tome 47 (2008) no. 2, pp. 215-239.

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The main result of the paper is describing all definable subsets in the group $\operatorname{Aut}\langle\mathbb Q,\le\rangle$ of all automorphisms of the natural ordering on the rational numbers, and also in groups of the form $\operatorname{Aut}_\mathbf I\langle\mathbb Q,\le\rangle$, where $\mathbf I$ is a Turing ideal consisting of elements of $\operatorname{Aut}\langle\mathbb Q,\le\rangle$ whose Turing degree is contained in $\mathbf I$. This description is properly a uniform method for proving definability of all basic properties appearing in works on the theory of groups $\operatorname{Aut}_\mathbf I\langle\mathbb Q,\le\rangle$, as well as definability of a number of new sets. Also, we describe automorphism groups for such groups $\operatorname{Aut}_\mathbf I\langle\mathbb Q,\le\rangle$ and state a number of structure properties for elementary subgroups in $\operatorname{Aut}\langle\mathbb Q,\le\rangle$.
Keywords: rational order
Mots-clés : automorphism group, definable set. 
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A. S. Morozov. Definable sets in automorphism groups of rational order. Algebra i logika, Tome 47 (2008) no. 2, pp. 215-239. http://geodesic.mathdoc.fr/item/AL_2008_47_2_a5/

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