A~jump inversion theorem for the semilattices of $\Sigma$-degrees
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 6 (2009), pp. 182-190.

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

For the semilattices of $\Sigma$-degrees of structures, we prove an analogue of the jump inversion theorem. As a corollary, we get similar result for the semilattices of degrees of of presentability of countable structures.
Keywords: computability, computable structures, admissible sets.
@article{SEMR_2009_6_a8,
     author = {A. I. Stukachev},
     title = {A~jump inversion theorem for the semilattices of $\Sigma$-degrees},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {182--190},
     publisher = {mathdoc},
     volume = {6},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2009_6_a8/}
}
TY  - JOUR
AU  - A. I. Stukachev
TI  - A~jump inversion theorem for the semilattices of $\Sigma$-degrees
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2009
SP  - 182
EP  - 190
VL  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2009_6_a8/
LA  - ru
ID  - SEMR_2009_6_a8
ER  - 
%0 Journal Article
%A A. I. Stukachev
%T A~jump inversion theorem for the semilattices of $\Sigma$-degrees
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2009
%P 182-190
%V 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2009_6_a8/
%G ru
%F SEMR_2009_6_a8
A. I. Stukachev. A~jump inversion theorem for the semilattices of $\Sigma$-degrees. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 6 (2009), pp. 182-190. http://geodesic.mathdoc.fr/item/SEMR_2009_6_a8/

[1] Yu. L. Ershov, Opredelimost i vychislimost, Nauchnaya kniga, Novosibirsk, 1996 | MR | Zbl

[2] S. S. Goncharov, B. Khusainov, “Slozhnost teorii vychislimykh kategorichnykh modelei”, Algebra i logika, 43 (2004), 650–665 | MR | Zbl

[3] O. V. Kudinov, A. I. Stukachev, Nekotorye zamechaniya o stepenyakh predstavimosti, rukopis

[4] A. S. Morozov, “Ob otnoshenii $\Sigma$-svodimosti mezhdu dopustimymi mnozhestvam”, Sib. mat. zhurnal, 45 (2004), 634–652 | MR | Zbl

[5] V. G. Puzarenko, “Ob odnoi svodimosti na dopustimykh mnozhestvakh”, Sib. mat. zhurnal, 50 (2009), 414–428 | MR

[6] A. I. Stukachev, “O stepenyakh predstavimosti modelei. I”, Algebra i logika, 46 (2007), 763–788 | MR | Zbl

[7] A. I. Stukachev, “O stepenyakh predstavimosti modelei. II”, Algebra i logika, 47 (2008), 108–126 | MR | Zbl

[8] J. Barwise, Admissible sets and structures, Springer-Verlag, Berlin, 1975 | MR | Zbl

[9] V. Baleva, “The jump operation for structure degrees”, Arch. Math. Logic, 45 (2006), 249–265 | DOI | MR | Zbl

[10] A. A. Soskova, “A jump inversion theorem for the degree spectra”, Computation and Logic in the Real World, LNCS, eds. S. B. Cooper, B. Loewe, A. Sorbi, Siena, 2007, 716–726 | Zbl

[11] A. A. Soskova, I. N. Soskov, “A jump inversion theorem for the degree spectra”, Journal of Logic and Computation, 19 (2009), 199–215 | DOI | MR | Zbl

[12] A. I. Stukachev, “Uniformization theorem for hereditary finite superstructures”, Siberian Advances in Mathematics, 7 (1997), 123–132 | MR