Geodesic
Initial segments of computable linear orders with computable natural relations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2016), pp. 15-26.

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We study the algorithmic complexity of natural relations on initial segments of computable linear orders. We prove that there exists a computable linear order with computable density relation such that its $\Pi^0_1$-initial segment has no computable presentation with computable density relation. We also prove that the same holds for right limit and left limit relations.
Keywords: linear orders, initial segments, density relation, right limit relation, left limit relation. 
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R. I. Bikmukhametov. Initial segments of computable linear orders with computable natural relations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2016), pp. 15-26. http://geodesic.mathdoc.fr/item/IVM_2016_6_a1/

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