Partial Decidable Presentations in Hyperarithmetic

Сибирский математический журнал

I. Sh. Kalimullin¹  V. G. Puzarenko² 

[1] Kazan (Volga Region) Federal University;Novosibirsk State University

关键词: numbering;    decidable numbering;    positive numbering;    computable numbering;    computable set;    computably enumerable set;    e-reducibility;    hyperarithmetic set;    constructible admissible set;   

DOI  :  10.1134/S0037446619030091

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

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.

【 授权许可】

CC BY