Partial Decidable Presentations in Hyperarithmetic

Abstract

© 2019, Pleiades Publishing, Inc. We study the problem of the existence of decidable and positive Π11- and Σ11-numberings of the families of Π11- and Σ11-cones with respect to inclusion. Some laws are found that reflect the presence of decidable computable Π11- and Σ11-numberings of these families in dependence on the analytical complexity of the set defining a cone.