Friedberg numberings of families of partial computable functionals

Sergey Ospichev

doi:10.33048/semi.2019.16.020

Friedberg numberings of families of partial computable functionals

Переведенное название: Фридберговы нумерации семейств частично вычислимых функционалов

Sergey Ospichev

Кафедра дискретной математики и информатики ММФ и СУНЦ

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

Аннотация

We consider computable numberings of families of partial computable functionals of finite types. We show, that if a family of all partial computable functionals of type 0 has a computable friedberg numbering, then family of all partial computable functionals of any given type also has computable friedberg numbering. Furthermore, for a type σ | τ there are infinitely many nonequivalent computable minimal nonpositive, positive nondecidable and friedberg numberings.

Переведенное название	Фридберговы нумерации семейств частично вычислимых функционалов
Язык оригинала	английский
Страницы (с-по)	331-339
Число страниц	9
Журнал	Siberian Electronic Mathematical Reports
Том	16
DOI	https://doi.org/10.33048/semi.2019.16.020
Состояние	Опубликовано - 1 янв 2019

Ключевые слова

Computable morphisms
Computable numberings
Friedberg numbering
Minimal numbering
Partial computable functionals
Positive numbering
Rogers semilattice

Доступ к документу

10.33048/semi.2019.16.020

Link to publication in Scopus

Fingerprint Подробные сведения о темах исследования «Фридберговы нумерации семейств частично вычислимых функционалов». Вместе они формируют уникальный семантический отпечаток (fingerprint).

Цитировать

@article{ad4c385c599a4b0a88d2a85c8cdb3c6d,

title = "Friedberg numberings of families of partial computable functionals",

abstract = "We consider computable numberings of families of partial computable functionals of finite types. We show, that if a family of all partial computable functionals of type 0 has a computable friedberg numbering, then family of all partial computable functionals of any given type also has computable friedberg numbering. Furthermore, for a type σ | τ there are infinitely many nonequivalent computable minimal nonpositive, positive nondecidable and friedberg numberings.",

keywords = "Computable morphisms, Computable numberings, Friedberg numbering, Minimal numbering, Partial computable functionals, Positive numbering, Rogers semilattice, partial computable functionals, computable morphisms, computable numberings, Rogers semilattice, minimal numbering, positive numbering, friedberg numbering",

author = "Sergey Ospichev",

year = "2019",

month = jan,

day = "1",

doi = "10.33048/semi.2019.16.020",

language = "English",

volume = "16",

pages = "331--339",

journal = "Siberian Electronic Mathematical Reports",

issn = "1813-3304",

publisher = "Sobolev Institute of Mathematics",

}

TY - JOUR

T1 - Friedberg numberings of families of partial computable functionals

AU - Ospichev, Sergey

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We consider computable numberings of families of partial computable functionals of finite types. We show, that if a family of all partial computable functionals of type 0 has a computable friedberg numbering, then family of all partial computable functionals of any given type also has computable friedberg numbering. Furthermore, for a type σ | τ there are infinitely many nonequivalent computable minimal nonpositive, positive nondecidable and friedberg numberings.

AB - We consider computable numberings of families of partial computable functionals of finite types. We show, that if a family of all partial computable functionals of type 0 has a computable friedberg numbering, then family of all partial computable functionals of any given type also has computable friedberg numbering. Furthermore, for a type σ | τ there are infinitely many nonequivalent computable minimal nonpositive, positive nondecidable and friedberg numberings.

KW - Computable morphisms

KW - Computable numberings

KW - Friedberg numbering

KW - Minimal numbering

KW - Partial computable functionals

KW - Positive numbering

KW - Rogers semilattice

KW - partial computable functionals

KW - computable morphisms

KW - computable numberings

KW - Rogers semilattice

KW - minimal numbering

KW - positive numbering

KW - friedberg numbering

UR - http://www.scopus.com/inward/record.url?scp=85066842368&partnerID=8YFLogxK

U2 - 10.33048/semi.2019.16.020

DO - 10.33048/semi.2019.16.020

M3 - Article

AN - SCOPUS:85066842368

VL - 16

SP - 331

EP - 339

JO - Siberian Electronic Mathematical Reports

JF - Siberian Electronic Mathematical Reports

SN - 1813-3304

ER -