Geodesic
Decomposability of low 2-computably enumerable degrees and Turing jumps in the Ershov hierarchy
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2010), pp. 58-66.

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

In this paper we prove the following theorem: For every notation of constructive ordinal, there exists a low 2-computably enumerable degree which is not splittable into two lower 2-computably enumerable degrees, whose jumps belong to the $\Delta$-level of the Ersov hierarchy that corresponds to this notation.
Keywords: low degrees, 2-computably enumerable degrees, Ershov hierarchy, Turing jumps, constructive ordinals. 
@article{IVM_2010_12_a5,
     author = {M. Kh. Faizrakhmanov},
     title = {Decomposability of low 2-computably enumerable degrees and {Turing} jumps in the {Ershov} hierarchy},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {58--66},
     publisher = {mathdoc},
     number = {12},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2010_12_a5/}
}
TY  - JOUR
AU  - M. Kh. Faizrakhmanov
TI  - Decomposability of low 2-computably enumerable degrees and Turing jumps in the Ershov hierarchy
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2010
SP  - 58
EP  - 66
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2010_12_a5/
LA  - ru
ID  - IVM_2010_12_a5
ER  - 
%0 Journal Article
%A M. Kh. Faizrakhmanov
%T Decomposability of low 2-computably enumerable degrees and Turing jumps in the Ershov hierarchy
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2010
%P 58-66
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2010_12_a5/
%G ru
%F IVM_2010_12_a5
M. Kh. Faizrakhmanov. Decomposability of low 2-computably enumerable degrees and Turing jumps in the Ershov hierarchy. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2010), pp. 58-66. http://geodesic.mathdoc.fr/item/IVM_2010_12_a5/

[1] Ershov Yu. L., “Ob odnoi ierarkhii mnozhestv, I”, Algebra i logika, 7:1 (1968), 47–74 | MR | Zbl

[2] Ershov Yu. L., “Ob odnoi ierarkhii mnozhestv, II”, Algebra i logika, 7:4 (1968), 15–47 | MR | Zbl

[3] Ershov Yu. L., “Ob odnoi ierarkhii mnozhestv, III”, Algebra i logika, 9:1 (1970), 34–51 | MR | Zbl

[4] Arslanov M. M., Ierarkhiya Ershova, Izd-vo Kazansk. un-ta, Kazan, 2007

[5] Arslanov M. M., “Strukturnye svoistva stepenei nizhe $0'$”, Izv. vuzov. Matematika, 1988, no. 7, 27–33 | MR | Zbl

[6] Downey R. G., “D. r. e. degrees and the nondiamond theorem”, Bull. Lond. Math. Soc., 21 (1989), 43–50 | DOI | MR | Zbl

[7] Lachlan A. H., “Lower bounds for pairs of recursively enumerable degrees”, Proc. Lond. Math. Soc. III Ser., 16 (1966), 537–569 | DOI | MR | Zbl

[8] Cooper S. B., Harrington L., Lachlan A. H., Lempp S., Soare R. I., “The d. r. e. degrees are not dense”, Ann. Pure Appl. Logic, 55:2 (1991), 125–151 | DOI | MR | Zbl

[9] Sacks G. E., “The recursively enumerable degrees are dense”, Ann. Math., 80:2 (1964), 300–312 | DOI | MR | Zbl

[10] Arslanov M., Cooper S. B., Li A., “There is no low maximal d. c. e. degree”, Math. Log. Q., 46:3 (2000), 409–416 ; “Corrigendum”, 50:6 (2004), 628–636 | 3.0.CO;2-P class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl | DOI | MR

[11] Welch L., A hierarchy of families of recursively enumerable degrees and a theorem of founding minimal pairs, Ph. D. Thesis, University of Illinois, Urbana, 1980 | MR