Monotone hulls for ${\mathcal N}\cap {\mathcal M}$

by Roslanowski and Shelah. [RoSh:972]
Periodica Math Hungarica, 2014
Using the method of decisive creatures ([KrSh:872]) 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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