Mycielski ideal and the perfect set theorem

Repický, Miroslav

doi:10.1090/S0002-9939-04-07360-5

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.

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