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Matematicheskie Zametki, 2012, Volume 91, Issue 6, Pages 840–852
DOI: https://doi.org/10.4213/mzm8544
(Mi mzm8544)
 

This article is cited in 2 scientific papers (total in 2 papers)

Effective Compactness and Sigma-Compactness

V. G. Kanovei, V. A. Lyubetskii

A. A. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences
Full-text PDF (574 kB) Citations (2)
References:
Abstract: Using the Gandy–Harrington topology and other methods of effective descriptive set theory, we prove several theorems about compact and σ-compact sets. In particular, it is proved that any Δ11-set A in the Baire space N either is an at most countable union of compact Δ11-sets (and hence is σ-compact) or contains a relatively closed subset homeomorphic to N (in this case, of course, A cannot be σ-compact).
Keywords: effective descriptive set theory, effectively compact, σ-compact, the Baire space, Gandy–Harrington topology, Δ11-set.
Received: 01.11.2009
Revised: 27.05.2011
English version:
Mathematical Notes, 2012, Volume 91, Issue 6, Pages 789–799
DOI: https://doi.org/10.1134/S0001434612050252
Bibliographic databases:
Document Type: Article
UDC: 510.225
Language: Russian
Citation: V. G. Kanovei, V. A. Lyubetskii, “Effective Compactness and Sigma-Compactness”, Mat. Zametki, 91:6 (2012), 840–852; Math. Notes, 91:6 (2012), 789–799
Citation in format AMSBIB
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Linking options:
  • https://www.mathnet.ru/eng/mzm8544
  • https://doi.org/10.4213/mzm8544
  • https://www.mathnet.ru/eng/mzm/v91/i6/p840
  • This publication is cited in the following 2 articles:
    1. Lyubetsky V.A. Seliverstov A.V., “A novel algorithm for solution of a combinatory set partitioning problem”, J. Commun. Technol. Electron., 61:6 (2016), 705–708  crossref  isi  elib  scopus
    2. V. G. Kanovei, V. A. Lyubetskii, “On Effective σ-Boundedness and σ-Compactness in Solovay's Model”, Math. Notes, 98:2 (2015), 273–282  mathnet  crossref  crossref  mathscinet  isi  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    References:51
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