Monotone hulls for N cap M
Abstract
Using the method of decisive creatures (math.LO/0601083) we show the consistency of "there is no increasing omega2 --chain of Borel sets and non(N)=non(M)= omega2=2omega". Hence, consistently, there are no monotone hulls for the ideal M cap N . This answers Balcerzak and Filipczak. Next we use FS iteration with partial memory to show that there may be monotone Borel hulls for the ideals M, N even if they are not generated by towers.
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