Monotone hulls for N cap M

Details Monotone hulls for N cap M Monotone hulls for N cap M

2010-07-30

arxiv.org/abs/1007.5368v1

Mathematics

Logic

Scientific paper

Using the method of decisive creatures (math.LO/0601083) we show the consistency of "there is no increasing omega_2 --chain of Borel sets and non(N)=non(M)= omega_2=2^omega". 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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