# complete partial orders do not add small subsets

Suppose $P$ is a $\kappa$-complete partial order in $\mathfrak{M}$. Then for any generic subset $G$, $\mathfrak{M}$ contains no bounded subsets of $\kappa$ which are not in $\mathfrak{M}$.

Title complete partial orders do not add small subsets CompletePartialOrdersDoNotAddSmallSubsets 2013-03-22 12:53:32 2013-03-22 12:53:32 Henry (455) Henry (455) 4 Henry (455) Theorem msc 03E40