### 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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