2019/04/04 by Goldstern, Martin, Kellner, Jakob, Mejía, Diego A. +1
#03E17 #03E35 #03E40 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.1904.02617
Given a forcing notion P that forces certain values to several classical cardinal characteristics of the reals, we show how we can compose P with a collapse (of a cardinal λ>κ to κ) such that the composition still forces the previous values to these characteristics. We also show how to force distinct values to \mathfrak m, \mathfrak p and \mathfrak h and also keeping all the values in Cichoń's diagram distint, using the Boolean Ultrapower method of arXiv:1708.03691 . (In arXiv:2006.09826 , the same was done for the newer Cichoń's Maximum construction, which avoids large cardinals.)