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@article{AL_2020_59_5_a5, author = {N. A. Bazhenov and M. Mustafa and S. S. Ospichev and M. M. Yamaleev}, title = {Numberings in the analytical hierarchy}, journal = {Algebra i logika}, pages = {594--599}, publisher = {mathdoc}, volume = {59}, number = {5}, year = {2020}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/AL_2020_59_5_a5/} }
N. A. Bazhenov; M. Mustafa; S. S. Ospichev; M. M. Yamaleev. Numberings in the analytical hierarchy. Algebra i logika, Tome 59 (2020) no. 5, pp. 594-599. http://geodesic.mathdoc.fr/item/AL_2020_59_5_a5/
[1] S. S. Goncharov, A. Sorbi, “Obobschenno-vychislimye numeratsii i netrivialnye polureshetki Rodzhersa”, Algebra i logika, 36:6 (1997), 621–641 | MR | Zbl
[2] Yu. L. Ershov, Teoriya numeratsii, Nauka, M., 1977 | MR
[3] S. A. Badaev, S. S. Goncharov, “Theory of numberings: open problems”, Computability theory and its applications, Contemp. Math., 257, eds. P. Cholak et al., Am. Math. Soc., Providence, RI, 2000, 23–38 | DOI | MR | Zbl
[4] S. Badaev, S. Goncharov, “Computability and numberings”, New computational paradigms. Changing conceptions of what is computable, eds. S. B. Cooper et al., Springer-Verlag, New York, NY, 2008, 19–34 | MR | Zbl
[5] J. C. Owings, Jr., “The meta-r.e. sets, but not the $\Pi^1_1$ sets, can be enumerated without repetition”, J. Symb. Log., 35:2 (1970), 223–229 | DOI | MR | Zbl
[6] S. A. Badaev, S. S. Goncharov, A. Corbi, “Tipy izomorfizmov polureshetok Rodzhersa semeistv iz razlichnykh urovnei arifmeticheskoi ierarkhii”, Algebra i logika, 45:6 (2006), 637–654 | MR | Zbl
[7] S. Yu. Podzorov, “Arifmeticheskie $m$-stepeni”, Sib. matem. zh., 49:6 (2008), 1391–1410 | MR | Zbl
[8] I. Herbert, S. Jain, S. Lempp, M. Mustafa, F. Stephan, “Reductions between types of numberings”, Ann. Pure Appl. Logic, 170:12 (2019), 102716, 25 pp. | DOI | MR | Zbl
[9] N. Bazhenov, S. Ospichev, M. Yamaleev, Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap., 2019 (to appear) , arXiv: 1912.05226 [math.LO]
[10] S. A. Badaev, S. S. Goncharov, S. Yu. Podzorov, A. Sorbi, “Algebraic properties of Rogers semilattices of arithmetical numberings”, Computability and models, eds. S. B. Cooper, S. S. Goncharov, Kluwer Academic/Plenum Publishers, New York, 2003, 45–77 | DOI | MR
[11] M. V. Dorzhieva, “Nerazreshimost elementarnykh teorii polureshetok Rodzhersa analiticheskoi ierarkhii”, Sib. elektron. matem. izv., 13 (2016), 148–153 http://semr.math.nsc.ru/v13/p148-153.pdf | MR | Zbl
[12] N. Bazhenov, M. Mustafa, Elementary theories of Rogers semilattices in the analytical hierarchy, submitted
[13] N. Bazhenov, M. Mustafa, Rogers semilattices in the analytical hierarchy: The case of finite families, submitted
[14] S. A. Badaev, S. S. Goncharov, A. Sorbi, “Isomorphism types and theories of Rogers semilattices of arithmetical numberings”, Computability and models, eds. S. B. Cooper, S. S. Goncharov, Kluwer Academic/Plenum Publishers, New York, 2003, 79–91 | DOI | MR
[15] T. Jech, Set Theory, Springer Monogr. Math., The third millenium edition, revised and expanded, Springer, Berlin, 2003 | MR | Zbl