  A set X which is a subset of the Cantor set has property (s) (Marczewski
(Spzilrajn)) iff for every perfect set P there exists a perfect set Q contained
in P such that Q is a subset of X or Q is disjoint from X. Suppose U is a
nonprincipal ultrafilter on omega. It is not difficult to see that if U is
preserved by Sacks forcing, i.e., it generates an ultrafilter in the generic
extension after forcing with the partial order of perfect sets, then U has
property (s) in the ground model. It is known that selective ultrafilters or
even P-points are preserved by Sacks forcing. On the other hand (answering a
question raised by Hrusak) we show that assuming CH (or more generally MA for
ctble posets) there exists an ultrafilter U with property (s) such that U does
not generate an ultrafilter in any extension which adds a new subset of omega.
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