Mycielski ideal and the perfect set theorem
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- by Miroslav Repický PDF
- Proc. Amer. Math. Soc. 132 (2004), 2141-2150 Request permission
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 $A\subseteq {}^\omega 2$ 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.References
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Additional Information
- Miroslav Repický
- Affiliation: Mathematical Institute of Slovak Academy of Sciences, Jesenná 5, 041 54 Košice, Slovakia
- Email: repicky@kosice.upjs.sk
- 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
- © Copyright 2004 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 132 (2004), 2141-2150
- MSC (2000): Primary 03E15; Secondary 03E17, 91A44
- DOI: https://doi.org/10.1090/S0002-9939-04-07360-5
- MathSciNet review: 2053988