A Version of $\kappa$-Miller Forcing

Heike Mildenberger, Saharon Shelah

Let $\kappa$ be an uncountable cardinal such that $2^{<\kappa }=\kappa$ or just $\mathrm{cf}(\kappa )>\omega$, $2^{2^{<\kappa }}=2^{\kappa }$, and $([\kappa {]}^{\kappa },\supseteq )$ collapses $2^{\kappa }$ to $\omega$. We show under these assumpt…