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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IVM_2016_6_a1,
     author = {R. I. Bikmukhametov},
     title = {Initial segments of computable linear orders with computable natural relations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {15--26},
     publisher = {mathdoc},
     number = {6},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_6_a1/}
}
TY  - JOUR
AU  - R. I. Bikmukhametov
TI  - Initial segments of computable linear orders with computable natural relations
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2016
SP  - 15
EP  - 26
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2016_6_a1/
LA  - ru
ID  - IVM_2016_6_a1
ER  - 
%0 Journal Article
%A R. I. Bikmukhametov
%T Initial segments of computable linear orders with computable natural relations
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2016
%P 15-26
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2016_6_a1/
%G ru
%F IVM_2016_6_a1
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/