Geodesic
Presentations of the successor relation of computably linear ordering
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2010), pp. 73-85 Cet article a éte moissonné depuis la source Math-Net.Ru

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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},
     year = {2010},
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     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/

[1] Harizanov V., Degree spectrum of a recursive relation on a recursive structure, PhD dissertation, University of Wisconsin, Madison, 1987

[2] Hirshfeldt D., “Degree spectra of relations on computable structures in the presence of $\Delta^0_2$ isomorphisms”, J. Symb. Logic, 67:2 (2002), 697–720 | DOI | MR

[3] Chubb J., Frolov A., Harizanov V., “Degree spectra of the successor relation of computable linear orderings”, Archive for Mathematical Logic, 48:1 (2009), 7–13 | DOI | MR | Zbl

[4] Downey R., Moses M., “Recursive linear orders with incomplete successivities”, Trans. Amer. Math. Soc., 326:2 (1991), 653–668 | DOI | MR | Zbl

[5] Soar R. I., Vychislimo perechislimye mnozhestva i stepeni, per. s angl., Kazansk. matem. o-vo, Kazan, 2000 | MR | Zbl