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LEFT-ORDERABLE COMPUTABLE GROUPS

Published online by Cambridge University Press:  05 February 2018

MATTHEW HARRISON-TRAINOR
MATTHEW HARRISON-TRAINOR*
Affiliation:
GROUP IN LOGIC AND THE METHODOLOGY OF SCIENCE UNIVERSITY OF CALIFORNIA BERKELEY, CA, USAE-mail:[email protected]: www.math.berkeley.edu/∼mattht
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Abstract

Downey and Kurtz asked whether every orderable computable group is classically isomorphic to a group with a computable ordering. By an order on a group, one might mean either a left-order or a bi-order. We answer their question for left-orderable groups by showing that there is a computable left-orderable group which is not classically isomorphic to a computable group with a computable left-order. The case of bi-orderable groups is left open.

Keywords

03D4503C57computable structure theorycomputable algebraordered groups
Type
Articles
Information
The Journal of Symbolic Logic , Volume 83 , Issue 1 , March 2018 , pp. 237 - 255
Copyright
Copyright © The Association for Symbolic Logic 2018 

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References

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