Geodesic
Presentations of the successor relation of computably linear ordering
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2010), pp. 73-85

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We prove that a nontrivial degree spectrum of the successor relation of either strongly $\eta$-like or non-$\eta$-like computable linear orderings is closed upward in the class of all computably enumerable degrees. We also show that the degree spectrum contains $\mathbf0$ if and only if either it is trivial or it contains all computably enumerable degrees.
Keywords: linear orderings, successor relation, Turing degree spectra, computable presentations. 
@article{IVM_2010_7_a6,
     author = {A. N. Frolov},
     title = {Presentations of the successor relation of computably linear ordering},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {73--85},
     publisher = {mathdoc},
     number = {7},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_7_a6/}
}
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A. N. Frolov. Presentations of the successor relation of computably linear ordering. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2010), pp. 73-85. http://geodesic.mathdoc.fr/item/IVM_2010_7_a6/