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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Mycielski ideal and the perfect set theorem


Author: Miroslav Repicky
Translated by:
Journal: Proc. Amer. Math. Soc. 132 (2004), 2141-2150
MSC (2000): Primary 03E15; Secondary 03E17, 91A44
Published electronically: January 23, 2004
MathSciNet review: 2053988
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Abstract: We make several observations on the Mycielski ideal and prove a version of the perfect set theorem concerning this ideal for analytic sets: If $A\subseteq{}^\omega2$ is an analytic set all projections of which are uncountable, then there is a perfect set $B\subseteq A$ a projection of which is the whole space. We also prove that (a modification of) an infinite game of Mycielski is determined for analytic sets.


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Additional Information

Miroslav Repicky
Affiliation: Mathematical Institute of Slovak Academy of Sciences, Jesenná 5, 04154 Košice, Slovakia
Email: repicky@kosice.upjs.sk

DOI: http://dx.doi.org/10.1090/S0002-9939-04-07360-5
PII: S 0002-9939(04)07360-5
Keywords: Mycielski ideal, analytic sets, perfect set theorem
Received by editor(s): August 21, 2002
Received by editor(s) in revised form: March 27, 2003
Published electronically: January 23, 2004
Additional Notes: This work was supported by a grant of Slovak Grant Agency VEGA 2/7555/20.
Communicated by: Alan Dow
Article copyright: © Copyright 2004 American Mathematical Society