Abstract:
In R. Downey's 1998 survey, the question was posed: describe order properties $P$ such that for any low linear order $L$, if $P(L)$ holds, then $L$ has a computable copy. This paper shows that the property of being scattered is not such a property. Namely, a low scattered linear order of rank $2$ with no computable copy is constructed.
Keywords:low linear order, scattered linear order, computable linear order.
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