Partial Decidable Presentations in Hyperarithmetic
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.
Keywordsnumbering decidable numbering positive numbering computable numbering computable set computably enumerable set e-reducibility hyperarithmetic set constructible admissible set
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