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Covering for category and trigonometric thin sets


Author: Peter Elias
Journal: Proc. Amer. Math. Soc. 131 (2003), 3241-3249
MSC (2000): Primary 03E75; Secondary 03E17, 40A30, 43A46
DOI: https://doi.org/10.1090/S0002-9939-03-06869-2
Published electronically: February 12, 2003
MathSciNet review: 1992865
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Abstract: In this work we consider several combinatorial principles satisfied for cardinals smaller than $\operatorname{cov} (\mathcal M)$, the covering number of the ideal of first category sets on real line. Using these principles we prove that there exist N$_0$-sets (similarly N-sets, A-sets) which cannot be covered by fewer than $\operatorname{cov}(\mathcal M)$ pD-sets (A-sets, N-sets, respectively). This improves the results of our previous paper (1997).


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Additional Information

Peter Elias
Affiliation: Mathematical Institute, Slovak Academy of Sciences, Grešákova 6, 04001 Košice, Slovakia
Email: elias@kosice.upjs.sk

DOI: https://doi.org/10.1090/S0002-9939-03-06869-2
Keywords: Covering, first category sets, meager sets, trigonometric thin sets, A-sets, N-sets, N$_0$-sets, pD-sets
Received by editor(s): October 23, 2001
Received by editor(s) in revised form: May 17, 2002
Published electronically: February 12, 2003
Additional Notes: The work on this paper was supported by grant 1/7555/20 of Slovak Grant Agency VEGA
Communicated by: Carl G. Jockusch, Jr.
Article copyright: © Copyright 2003 American Mathematical Society

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