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ON FOREMAN’S MAXIMALITY PRINCIPLE
Published online by Cambridge University Press: 29 September 2016
Abstract
In this paper, we consider Foreman’s maximality principle, which says that any nontrivial forcing notion either adds a new real or collapses some cardinals. We prove the consistency of some of its consequences. We observe that it is consistent that every c.c.c. forcing adds a real and that for every uncountable regular cardinal κ, every κ-closed forcing of size 2<κ collapses some cardinal.
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- Copyright © The Association for Symbolic Logic 2016
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