Left-orderable Computable Groups
Matthew Harrison-Trainor
TL;DR
This paper constructs a computable left-orderable group that cannot be classically isomorphic to any computable group with a computable left-order, addressing a question in the theory of computable groups.
Contribution
It demonstrates the existence of a computable left-orderable group lacking a computable left-order, providing a counterexample to a previously open question.
Findings
Existence of a computable left-orderable group not isomorphic to any computable group with a computable left-order
Addresses a question posed by Downey and Kurtz
Advances understanding of computability in group orderings
Abstract
We answer a question of Downey and Kurtz on 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.
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