On Foreman's maximality principle

Mohammad Golshani; Yair Hayut

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arXiv · 1502.07470

On Foreman's maximality principle

Mohammad Golshani·Yair Hayut

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Abstract

In this paper we consider the Foreman's maximality principle, which says that any non-trivial forcing notion either adds a new real or collapses some cardinals. We prove the consistency of some of its consequences. We prove that it is consistent that every $c.c.c.$ forcing adds a real and that for every uncountable regular cardinal $\kappa$, every $\kappa$-closed forcing of size $2^{<\kappa}$ collapses some cardinals.

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Mohammad Golshani, Yair Hayut. 2015-02-26. On Foreman's maximality principle. https://arxiv.org/abs/1502.07470

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