Partial Decidable Presentations in Hyperarithmetic
ISKANDER SH. KALIMULLIN, V. G. Puzarenko, M. Kh. Faĭzrahmanov · Siberian Mathematical Journal · 2019
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.