Geodesic
A note on $\Delta_2^0$-spectra of linear orderings and degree spectra of the successor relation
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2013), pp. 74-78.

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

In this paper we construct linear orderings whose $\Delta_2^0$-spectra coincide with classes of all high$_0$ and high$_1$ degrees, respectively. We also prove that there exists a computable linear ordering such that its degree spectrum of the successor relation coincides with a fixed nonempty class of degrees which represents a $\Sigma_1^0$-spectrum of some $\emptyset'$-computable linear ordering.
Keywords: linear orderings, degree spectra of the successor relation.
Mots-clés : spectra 
@article{IVM_2013_11_a6,
     author = {A. N. Frolov},
     title = {A note on $\Delta_2^0$-spectra of linear orderings and degree spectra of the successor relation},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {74--78},
     publisher = {mathdoc},
     number = {11},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_11_a6/}
}
TY  - JOUR
AU  - A. N. Frolov
TI  - A note on $\Delta_2^0$-spectra of linear orderings and degree spectra of the successor relation
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2013
SP  - 74
EP  - 78
IS  - 11
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2013_11_a6/
LA  - ru
ID  - IVM_2013_11_a6
ER  - 
%0 Journal Article
%A A. N. Frolov
%T A note on $\Delta_2^0$-spectra of linear orderings and degree spectra of the successor relation
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2013
%P 74-78
%N 11
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2013_11_a6/
%G ru
%F IVM_2013_11_a6
A. N. Frolov. A note on $\Delta_2^0$-spectra of linear orderings and degree spectra of the successor relation. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 11 (2013), pp. 74-78. http://geodesic.mathdoc.fr/item/IVM_2013_11_a6/

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

[2] Rosenstein J. R., Linear orderings, Pure and Applied Mathematics, 98, Academic Press Inc., Hartcourt Brace Jovanovich Publishers, New York–London, 1982 | MR | Zbl

[3] Downey R. G., Recursion theory and linear orderings, Handbook of computable algebra, eds. Yu. L. Ershov, S. S. Goncharov, A. Nerode, J. B. Remmel, 1998

[4] Frolov A., Harizanov V., Kalimullin I., Kudinov O., Miller R., “Spectra of $\mathrm{high}_n$ and $\mathrm{nonlow}_n$ degrees”, J. Logic Computation, 22:4 (2012), 745–754 | DOI | MR | Zbl

[5] Miller R., “The $\Delta_2^0$ spectrum of a linear ordering”, J. Symbolic Logic, 66:2 (2001), 470–486 | DOI | MR | Zbl

[6] Frolov A. N., “$\Delta_2^0$-kopii lineinykh poryadkov”, Algebra i logika, 45:3 (2006), 354–370 | MR | Zbl

[7] Frolov A. N., “Predstavleniya otnosheniya sosedstva vychislimogo lineinogo poryadka”, Izv. vuzov. Matem., 2010, no. 7, 73–88 | MR

[8] Downey R., Lempp S., Wu G., “On the complexity of the successivity relation in computable linear orderings”, J. Math. Logic, 83:10 (2010), 83–99 | DOI | MR | Zbl

[9] Jockusch C. G. (jr.), Soare R. I., “Degrees of orderings not isomorphic to recursive linear orderings”, Ann. Pure Appl. Logic, 52:1–2 (1991), 39–64 | DOI | MR | Zbl

[10] Downey R. G., Knight J. F., “Orderings with $\alpha$-th jump degree $0^{(\alpha)}$”, Proc. Amer. Math. Soc., 114:2 (1992), 545–552 | MR | Zbl

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