Abstract
We construct the example of an admissible set \(\mathbb{A}\) such that there exists a positive computable \(\mathbb{A}\)-numbering of the family of all \(\mathbb{A}\)-c.e. sets, whereas any negative computable \(\mathbb{A}\)-numberings are absent.
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Dedicated to the 80th birthday of Academician Yu. L. Ershov, the founder of the areas of semantic programming and computability on admissible structures.
Russian Text © The Author(s), 2020, published in Sibirskii Matematicheskii Zhurnal, 2020, Vol. 61, No. 3, pp. 607–621.
I. Sh. Kalimullin was supported by the Russian Science Foundation (Grant 18-11-00028). Also he is funded by the Russian Government as a Federal Professor of Mathematics. V. G. Puzarenko was supported by the Mathematical Center in Akademgorod, the Ministry of Education and Science of the Russian Federation (Agreement 075-15-2019-1613), and the State Task to the Sobolev Institute of Mathematics (Project 0314-2019-0003). The work of M. Kh. Faizrahmanov was carried out in the framework of the program of support of the Mathematical Center of the Volga Region Federal District.
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Kalimullin, I.S., Puzarenko, V.G. & Faizrahmanov, M.K. Positive Numberings in Admissible Sets. Sib Math J 61, 478–489 (2020). https://doi.org/10.1134/S003744662003009X
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DOI: https://doi.org/10.1134/S003744662003009X