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Mat. Zametki, 2012, Volume 91, Issue 6, Pages 840–852 (Mi mz8544)  

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

Abstract: Using the Gandy–Harrington topology and other methods of effective descriptive set theory, we prove several theorems about compact and $\sigma$-compact sets. In particular, it is proved that any $\Delta_1^1$-set $A$ in the Baire space $\mathscr N$ either is an at most countable union of compact $\Delta_1^1$-sets (and hence is $\sigma$-compact) or contains a relatively closed subset homeomorphic to $\mathscr N$ (in this case, of course, $A$ cannot be $\sigma$-compact).

Keywords: effective descriptive set theory, effectively compact, $\sigma$-compact, the Baire space, Gandy–Harrington topology, $\Delta^1_1$-set

DOI: https://doi.org/10.4213/mzm8544

Full text: PDF file (574 kB)
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English version:
Mathematical Notes, 2012, 91:6, 789–799

Bibliographic databases:

Document Type: Article
UDC: 510.225
Received: 01.11.2009
Revised: 27.05.2011

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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  • https://doi.org/10.4213/mzm8544
  • http://mi.mathnet.ru/eng/mz/v91/i6/p840

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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. Lyubetskii, “On Effective $\sigma$-Boundedness and $\sigma$-Compactness in Solovay's Model”, Math. Notes, 98:2 (2015), 273–282  mathnet  crossref  crossref  mathscinet  isi  elib
    2. 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
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