Abstract
We consider a version of κ -Miller forcing on an uncountable cardinal κ . We show that under 2<κ = κ this forcing collapses 2κ to ω and adds a κ -Cohen real. The same holds under the weaker assumptions that cf (κ) > ω , 22<κ = 2κ , and forcing with ([κ]κ, ⊆ ) collapses 2κ to ω .