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Mat. Zametki, 2017, Volume 102, Issue 3, Pages 369–382 (Mi mz10842)  

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

A Countable Definable Set Containing no Definable Elements

V. G. Kanoveiab, V. A. Lyubetskiia

a Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute), Moscow
b Russian University of Transport

Abstract: The consistency of the existence of a countable definable set of reals, containing no definable elements, is established. The model, where such a set exists, is obtained by means of a countable product of Jensen's forcing with finite support.

Keywords: countable sets, definable elements, Jensen's forcing.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00006
17-01-00705
Russian Science Foundation 14-50-00150
The work of V. G. Kanovei was supported by the Russian Foundation for Basic Research under grants 13-01-00006 and 17-01-00705. The work of V. A. Lyubetsky was supported by the Russian Science Foundation under grant 14-50-00150.


DOI: https://doi.org/10.4213/mzm10842

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English version:
Mathematical Notes, 2017, 102:3, 338–349

Bibliographic databases:

Document Type: Article
UDC: 510.225+510.223
Received: 16.06.2015
Revised: 14.04.2017

Citation: V. G. Kanovei, V. A. Lyubetskii, “A Countable Definable Set Containing no Definable Elements”, Mat. Zametki, 102:3 (2017), 369–382; Math. Notes, 102:3 (2017), 338–349

Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm10842
  • http://mi.mathnet.ru/eng/mz/v102/i3/p369

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. G. Kanovei, V. A. Lyubetsky, “Non-uniformizable sets of second projective level with countable cross-sections in the form of Vitali classes”, Izv. Math., 82:1 (2018), 61–90  mathnet  crossref  crossref  adsnasa  isi  elib
    2. Kanovei V., Lyubetsky V., “Definable E-0 Classes At Arbitrary Projective Levels”, Ann. Pure Appl. Log., 169:9 (2018), 851–871  crossref  mathscinet  zmath  isi  scopus
  • Математические заметки Mathematical Notes
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