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Problemy Peredachi Informatsii, 2010, Volume 46, Issue 4, Pages 83–90 (Mi ppi2027)  
This article is cited in 2 scientific papers (total in 2 papers)

Large Systems

Complete and incomplete Boolean degrees

S. S. Marchenkov

M. V. Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics
Full-text PDF (170 kB) Citations (2)
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Abstract: We study the partially ordered set of Boolean $P_2$-degrees. We introduce the notions of complete and incomplete Boolean degrees. We show that for each complete $P_2$-degree there exist both a countable decreasing chain of $P_2$-degrees and a countable antichain of $P_2$-degrees. We prove that above each incomplete $P_2$-degree there is a continuum of $P_2$-degrees. Thus, in total we show that in the partially ordered set of $P_2$-degrees there are no maximal elements.
Received: 24.05.2010
Revised: 13.09.2010
English version:
Problems of Information Transmission, 2010, Volume 46, Issue 4, Pages 346–352
DOI: https://doi.org/10.1134/S0032946010040058
Bibliographic databases:
Document Type: Article
UDC: 621.391.1+519.71
Language: Russian
Citation: S. S. Marchenkov, “Complete and incomplete Boolean degrees”, Probl. Peredachi Inf., 46:4 (2010), 83–90; Problems Inform. Transmission, 46:4 (2010), 346–352
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Проблемы передачи информации Problems of Information Transmission
     
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