Annals of Pure and Applied Logic 161 (9):1134-1143 (2010)

Valentina Harizanov
George Washington University
We investigate computability theoretic and topological properties of spaces of orders on computable orderable groups. A left order on a group G is a linear order of the domain of G, which is left-invariant under the group operation. Right orders and bi-orders are defined similarly. In particular, we study groups for which the spaces of left orders are homeomorphic to the Cantor set, and their Turing degree spectra contain certain upper cones of degrees. Our approach unifies and extends Sikora’s [28] investigation of orders on groups in topology and Solomon’s [31] investigation of these orders in computable algebra. Furthermore, we establish that a computable free group Fn of rank n>1 has a bi-order in every Turing degree
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DOI 10.1016/j.apal.2010.01.004
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References found in this work BETA

Reverse Mathematics and Fully Ordered Groups.Reed Solomon - 1998 - Notre Dame Journal of Formal Logic 39 (2):157-189.
Recursion Theory and Ordered Groups.R. G. Downey & Stuart A. Kurtz - 1986 - Annals of Pure and Applied Logic 32:137-151.
Degree Spectra of Relations on Computable Structures.Denis R. Hirschfeldt - 2000 - Bulletin of Symbolic Logic 6 (2):197-212.
Recursively Enumerable Vector Spaces.G. Metakides - 1977 - Annals of Mathematical Logic 11 (2):147.

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Citations of this work BETA

Degrees of Orders on Torsion-Free Abelian Groups.Asher M. Kach, Karen Lange & Reed Solomon - 2013 - Annals of Pure and Applied Logic 164 (7-8):822-836.

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