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Mycielski ideal and the perfect set theorem

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 C ω 2 is an analytic set all projections of which are uncountable, then there is a perfect set B C 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.