Historic forcing for {\rm Depth}

by Roslanowski and Shelah. [RoSh:733]
Colloquium Math, 2001
We show that, consistently, for some regular cardinals theta < lambda, there exist a Boolean algebra B such that |B|= lambda^+ and for every subalgebra B' subseteq B of size lambda^+ we have Depth (B')= theta .


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