Families Without Minimal Numberings

K. Sh Abeshev; S. A. Badaev; M. Mustafa

doi:10.1007/s10469-014-9290-9

Families Without Minimal Numberings

K. Sh Abeshev, S. A. Badaev, M. Mustafa

Al Farabi Kazakh National University

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

It is proved that for any nonzero computable ordinal and its arbitrary notation a, there exists a Σ_a^{− 1}-computable family without minimal computable numberings.

Original language	English
Pages (from-to)	271-286
Number of pages	16
Journal	Algebra and Logic
Volume	53
Issue number	4
DOIs	https://doi.org/10.1007/s10469-014-9290-9
Publication status	Published - Sept 2014
Externally published	Yes

Keywords

Ershov hierarchy
computable numbering
minimal numbering

ASJC Scopus subject areas

Analysis
Logic
Algebra and Number Theory

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10.1007/s10469-014-9290-9

Cite this

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title = "Families Without Minimal Numberings",

abstract = "It is proved that for any nonzero computable ordinal and its arbitrary notation a, there exists a Σa− 1-computable family without minimal computable numberings.",

keywords = "Ershov hierarchy, computable numbering, minimal numbering",

author = "Abeshev, \{K. Sh\} and Badaev, \{S. A.\} and M. Mustafa",

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year = "2014",

month = sep,

doi = "10.1007/s10469-014-9290-9",

language = "English",

volume = "53",

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AU - Abeshev, K. Sh

AU - Badaev, S. A.

AU - Mustafa, M.

PY - 2014/9

Y1 - 2014/9

N2 - It is proved that for any nonzero computable ordinal and its arbitrary notation a, there exists a Σa− 1-computable family without minimal computable numberings.

AB - It is proved that for any nonzero computable ordinal and its arbitrary notation a, there exists a Σa− 1-computable family without minimal computable numberings.

KW - Ershov hierarchy

KW - computable numbering

KW - minimal numbering

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DO - 10.1007/s10469-014-9290-9

M3 - Article

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SN - 0002-5232

VL - 53

SP - 271

EP - 286

JO - Algebra and Logic

JF - Algebra and Logic

IS - 4

ER -

Families Without Minimal Numberings

Abstract

Keywords

ASJC Scopus subject areas

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