Degrees of orders on torsion-free Abelian groups

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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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

Countable Algebra and Set Existence Axioms.Harvey M. Friedman - 1983 - Annals of Pure and Applied Logic 25 (2):141.
Recursion Theory and Ordered Groups.R. G. Downey & Stuart A. Kurtz - 1986 - Annals of Pure and Applied Logic 32:137-151.
Degree Spectra of Intrinsically C.E. Relations.Denis R. Hirschfeldt - 2001 - Journal of Symbolic Logic 66 (2):441-469.
Graph Colorings and Recursively Bounded Π10-Classes.J. B. Remmel - 1986 - Annals of Pure and Applied Logic 32:185-194.
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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