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Algebra i logika, 2009, Volume 48, Number 1, Pages 31–53 (Mi al389)  
This article is cited in 20 scientific papers (total in 20 papers)

Reducibility on families

I. Sh. Kalimullina, V. G. Puzarenkob

a Department of Algebra and Mathematical Logics, N. G. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University, Kazan, Russia
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
Full-text PDF (273 kB) Citations (20)
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Abstract: A reducibility on families of subsets of natural numbers is introduced which allows the family per se to be treated without its representation by natural numbers being fixed. This reducibility is used to study a series of problems both in classical computability and on admissible sets: for example, describing index sets of families belonging to $\Sigma_3^0 $, generalizing Friedberg's completeness theorem for a suitable reducibility on admissible sets, etc.
Keywords: family of subsets of natural numbers, admissible set, reducibility.
Received: 29.11.2007
Revised: 30.10.2008
English version:
Algebra and Logic, 2009, Volume 48, Issue 1, Pages 20–32
DOI: https://doi.org/10.1007/s10469-009-9037-1
Bibliographic databases:
UDC: 510.5
Language: Russian
Citation: I. Sh. Kalimullin, V. G. Puzarenko, “Reducibility on families”, Algebra Logika, 48:1 (2009), 31–53; Algebra and Logic, 48:1 (2009), 20–32
Citation in format AMSBIB
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    • This publication is cited in the following 20 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Алгебра и логика Algebra and Logic
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    Full-text PDF :192
    References:93
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