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Sibirsk. Mat. Zh., 2011, Volume 52, Number 5, Pages 1074–1086 (Mi smj2259)  

This article is cited in 3 scientific papers (total in 3 papers)

An effective minimal encoding of uncountable sets

V. G. Kanovei, V. A. Lyubetsky

Kharkevich Institute for Information Transmission Problems, Moscow, Russia

Abstract: We propose a method for encoding sets of the countable ordinals by generic reals which preserves cardinality and enjoys the property of minimality over the encoded set.
For $W\subseteq\omega_1$ there is a cardinal-preserving generic extension $L[W][x]$ of the class $L[W]$ by a generic real $x$ such that $W$ belongs to the class $L[x]$, i.e., $W$ is Gödel constructible with respect to $x$, while $x$ itself is minimal over $L[W]$.

Keywords: forcing, minimal encoding, relatively constructible set.

Full text: PDF file (371 kB)
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English version:
Siberian Mathematical Journal, 2011, 52:5, 854–863

Bibliographic databases:

Document Type: Article
UDC: 510.223
Received: 14.08.2009

Citation: V. G. Kanovei, V. A. Lyubetsky, “An effective minimal encoding of uncountable sets”, Sibirsk. Mat. Zh., 52:5 (2011), 1074–1086; Siberian Math. J., 52:5 (2011), 854–863

Citation in format AMSBIB
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\by V.~G.~Kanovei, V.~A.~Lyubetsky
\paper An effective minimal encoding of uncountable sets
\jour Sibirsk. Mat. Zh.
\yr 2011
\vol 52
\issue 5
\pages 1074--1086
\mathnet{http://mi.mathnet.ru/smj2259}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2908128}
\transl
\jour Siberian Math. J.
\yr 2011
\vol 52
\issue 5
\pages 854--863
\crossref{https://doi.org/10.1134/S0037446611050107}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-80155151863}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. G. Kanovei, V. A. Lyubetsky, “Generalization of one construction by Solovay”, Siberian Math. J., 56:6 (2015), 1072–1079  mathnet  crossref  crossref  mathscinet  isi  elib
    2. Golshani M., Kanovei V., Lyubetsky V., “a Groszek-Laver Pair of Undistinguishable E-0-Classes”, Math. Log. Q., 63:1-2 (2017), 19–31  crossref  mathscinet  isi  scopus
    3. V. G. Kanovei, V. A. Lyubetskii, “A Countable Definable Set Containing no Definable Elements”, Math. Notes, 102:3 (2017), 338–349  mathnet  crossref  crossref  mathscinet  isi  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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