2015/02/26 by Golshani, Mohammad, Hayut, Yair
#FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1502.07470
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 κ, every κ-closed forcing of size 2^