Changing cofinalities and collapsing cardinals in models of set theory Original Research Article

If a~cardinal κ1, regular in the ground model M, is collapsed in the extension N to a~cardinal κ0 and its new cofinality, ρ, is less than κ0, then, under some additional assumptions, each cardinal λ>κ1 less than cc(P(κ1)/[κ1]<κ1) is collapsed to κ0 as well. If in addition N=M[f], where View the MathML source is an unbounded mapping, then N is a~|λ|=κ0-minimal extension. This and similar results are applied to generalized forcing notions of Bukovský and Namba.