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Algebra i logika, 2015, Volume 54, Number 3, Pages 305–314
DOI: https://doi.org/10.17377/alglog.2015.54.301 (Mi al695) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Ideals without minimal elements in Rogers semilattices

A. A. Issakhov

Al-Farabi Kazakh National University, Al-Farabi Ave. 71, Alma-Ata, 050038, Kazakhstan
Full-text PDF (136 kB) Citations (6)
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DOI: https://doi.org/10.17377/alglog.2015.54.301
Abstract: We prove a criterion for the existence of a minimal numbering, which is reducible to a given numbering of an arbitrary set. The criterion is used to show that, for any infinite $A$-computable family $F$ of total functions, where $\varnothing'\le_TA$, the Rogers semilattice $\mathcal R_A(F)$ of $A$-computable numberings for $F$ contains an ideal without minimal elements.
Keywords: minimal numbering, $A$-computable numbering, Rogers semilattice, ideal.
Received: 06.11.2014
English version:
Algebra and Logic, 2015, Volume 54, Issue 3, Pages 197–203
DOI: https://doi.org/10.1007/s10469-015-9340-y
Bibliographic databases:
Document Type: Article
UDC: 510.54
Language: Russian
Citation: A. A. Issakhov, “Ideals without minimal elements in Rogers semilattices”, Algebra Logika, 54:3 (2015), 305–314; Algebra and Logic, 54:3 (2015), 197–203
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и логика Algebra and Logic
     
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