Geodesic
Infinite family of $\Sigma_a^{-1}$-Sets with only One Computable Numbering
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 2, pp. 89-92 Cet article a éte moissonné depuis la source Math-Net.Ru

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There was constructed example of infinite family of $\Sigma^{-1}_{a}$-sets with only one $\Sigma^{-1}_{a}$-computable numbering, $a$ is constructive ordinal.
Keywords: computable numbering, Ershov's hierarchy. 
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S. S. Ospichev. Infinite family of $\Sigma_a^{-1}$-Sets with only One Computable Numbering. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 11 (2011) no. 2, pp. 89-92. http://geodesic.mathdoc.fr/item/VNGU_2011_11_2_a7/

[1] Maltsev A. I., Algoritmy i rekursivnye funktsii, Nauka, M., 1965 | MR

[2] Ershov Yu. L., Teoriya numeratsii, Nauka, M., 1977 | MR

[3] Ershov Yu. L., “Theory of Numberings”, Handbook of Computability Theory, ed. E. R. Griffor, North-Holland, Amsterdam, 1999, 473–503 | DOI | MR

[4] Goncharov S. S., Sorbi A., “Obobschenno vychislimye numeratsii i netrivialnye polureshetki Rodzhersa”, Algebra i logika, 36:6 (1997), 621–641 | MR | Zbl

[5] Arslanov M. M., Ierarkhiya Ershova, Kazan, 2007

[6] Goncharov S. S., Lempp S., Solomon D. R., “Fridbergovskie numeratsii semeistv $n$-vychislimo perechislimykh mnozhestv”, Algebra i logika, 41:2 (2002), 143–154 | MR | Zbl

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