Partial Decidable Presentations in Hyperarithmetic


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We study the problem of the existence of decidable and positive \(\Pi_1^1\)- and \(\Sigma_1^1\)-numberings of the families of \(\Pi_1^1\)- and \(\Sigma_1^1\)-cones with respect to inclusion. Some laws are found that reflect the presence of decidable computable \(\Pi_1^1\)- and \(\Sigma_1^1\)-numberings of these families in dependence on the analytical complexity of the set defining a cone.

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I. Kalimullin

Kazan (Volga Region) Federal University

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Email: ikalimul@gmail.com
俄罗斯联邦, Kazan

V. Puzarenko

Sobolev Institute of Mathematics

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Email: vagrig@math.nsc.ru
俄罗斯联邦, Novosibirsk

M. Faizrahmanov

Kazan (Volga Region) Federal University

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Email: marat.faizrahmanov@gmail.com
俄罗斯联邦, Kazan

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