Degrees of orders on torsion-free Abelian groups

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Annals of Pure and Applied Logic 164 (7-8):822-836 (2013)
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Abstract

We show that if H is an effectively completely decomposable computable torsion-free abelian group, then there is a computable copy G of H such that G has computable orders but not orders of every degree

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10.1016/j.apal.2013.01.005

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Citations of this work

Computable Abelian groups.Alexander G. Melnikov - 2014 - Bulletin of Symbolic Logic 20 (3):315-356,.
Orders on computable rings.Huishan Wu - 2020 - Mathematical Logic Quarterly 66 (2):126-135.

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References found in this work

Recursion theory and ordered groups.R. G. Downey & Stuart A. Kurtz - 1986 - Annals of Pure and Applied Logic 32:137-151.
Graph colorings and recursively bounded Π10-classes.J. B. Remmel - 1986 - Annals of Pure and Applied Logic 32:185-194.
Countable algebra and set existence axioms.Harvey M. Friedman - 1983 - Annals of Pure and Applied Logic 25 (2):141.
Degree spectra of intrinsically C.e. Relations.Denis R. Hirschfeldt - 2001 - Journal of Symbolic Logic 66 (2):441-469.
Every recursive boolean algebra is isomorphic to one with incomplete atoms.Rod Downey - 1993 - Annals of Pure and Applied Logic 60 (3):193-206.

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