### Аннотация

The objects considered here serve both as generalizations of numberings studied in [1] and as particular versions of A-numberings, where 픸 is a suitable admissible set, introduced in [2] (in view of the existence of a transformation realizing the passage from e-degrees to admissible sets [3]). The key problem dealt with in the present paper is the existence of Friedberg (single-valued computable) and positive presentations of families. In [3], it was stated that the above-mentioned transformation preserves the majority of properties treated in descriptive set theory. However, it is not hard to show that it also respects the positive (negative, decidable, single-valued) presentations. Note that we will have to extend the concept of a numbering and, in the general case, consider partial maps rather than total ones. The given effect arises under the passage from a hereditarily finite superstructure to natural numbers, since a computable function (in the sense of a hereditarily finite superstructure) realizing an enumeration of the hereditarily finite superstructure for nontotal sets is necessarily a partial function.

Язык оригинала | английский |
---|---|

Страницы (с-по) | 320-323 |

Число страниц | 4 |

Журнал | Algebra and Logic |

Том | 57 |

Номер выпуска | 4 |

DOI | |

Состояние | Опубликовано - 1 сен 2018 |

## Fingerprint Подробные сведения о темах исследования «Positive Presentations of Families in Relation to Reducibility with Respect to Enumerability». Вместе они формируют уникальный семантический отпечаток (fingerprint).

## Цитировать

*Algebra and Logic*,

*57*(4), 320-323. https://doi.org/10.1007/s10469-018-9503-8