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Sibirskii Matematicheskii Zhurnal, 2005, Volume 46, Number 1, Pages 185–208 (Mi smj951)  

This article is cited in 22 scientific papers (total in 22 papers)

Computability in special models

V. G. Puzarenko

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
References:
Abstract: We study some properties of descriptive set theory which translate from the ideals of enumerability degrees to admissible sets. We show that the reduction principle fails in the admissible sets corresponding to nonprincipal ideals and possessing the minimality property and that the properties of existence of a universal function, separation, and total extension translate from the ideals to some special classes of admissible sets. We first give some examples of the admissible sets satisfying the total extension principle. In addition, we define a broad subclass of admissible sets admitting no decidable computable numberings of the family of all computably enumerable subsets. We mostly discuss the minimal classes of admissible sets corresponding to the nonprincipal ideals of enumerability degrees.
Keywords: admissible set, ideal, $e$-reducibility, computability, descriptive set theory, Friedberg numbering.
Received: 29.10.2004
English version:
Siberian Mathematical Journal, 2005, Volume 46, Issue 1, Pages 148–165
DOI: https://doi.org/10.1007/s11202-005-0016-z
Bibliographic databases:
UDC: 510.5
Language: Russian
Citation: V. G. Puzarenko, “Computability in special models”, Sibirsk. Mat. Zh., 46:1 (2005), 185–208; Siberian Math. J., 46:1 (2005), 148–165
Citation in format AMSBIB
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\by V.~G.~Puzarenko
\paper Computability in special models
\jour Sibirsk. Mat. Zh.
\yr 2005
\vol 46
\issue 1
\pages 185--208
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2141313}
\zmath{https://zbmath.org/?q=an:1095.03030}
\transl
\jour Siberian Math. J.
\yr 2005
\vol 46
\issue 1
\pages 148--165
\crossref{https://doi.org/10.1007/s11202-005-0016-z}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000227076100016}
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  • https://www.mathnet.ru/eng/smj/v46/i1/p185
  • This publication is cited in the following 22 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский математический журнал Siberian Mathematical Journal
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