Computable Numberings of Families of Infinite Sets

M. V. Dorzhieva

doi:10.1007/s10469-019-09540-4

Computable Numberings of Families of Infinite Sets

M. V. Dorzhieva

Кафедра общей информатики ФИТ

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

Аннотация

We state the following results: the family of all infinite computably enumerable sets has no computable numbering; the family of all infinite Π11 sets has no Π11 -computable numbering; the family of all infinite Σ21 sets has no Σ21 -computable numbering. For k > 2, the existence of a Σk1 -computable numbering for the family of all infinite Σk1 sets leads to the inconsistency of ZF.

Язык оригинала	английский
Страницы (с-по)	224-231
Число страниц	8
Журнал	Algebra and Logic
Том	58
Номер выпуска	3
DOI	https://doi.org/10.1007/s10469-019-09540-4
Состояние	Опубликовано - 1 июл 2019

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10.1007/s10469-019-09540-4

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AB - We state the following results: the family of all infinite computably enumerable sets has no computable numbering; the family of all infinite Π11 sets has no Π11 -computable numbering; the family of all infinite Σ21 sets has no Σ21 -computable numbering. For k > 2, the existence of a Σk1 -computable numbering for the family of all infinite Σk1 sets leads to the inconsistency of ZF.

KW - analytical hierarchy

KW - computability

KW - computable numberings

KW - Friedberg numbering

KW - Gödel’s axiom of constructibility

KW - Godel's axiom of constructibility

KW - AXIOM

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Computable Numberings of Families of Infinite Sets

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