Perfect sets and collapsing continuum
نویسنده
چکیده
Under Martin’s axiom, collapsing of the continuum by Sacks forcing S is characterized by the additivity of Marczewski’s ideal (see [4]). We show that the same characterization holds true if d = c proving that under this hypothesis there are no small uncountable maximal antichains in S. We also construct a partition of 2 into c perfect sets which is a maximal antichain in S and show that s-sets are exactly (subsets of) selectors of maximal antichains of perfect sets.
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