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
Canonical name	CompletePartialOrdersDoNotAddSmallSubsets
Date of creation	2013-03-22 12:53:32
Last modified on	2013-03-22 12:53:32
Owner	Henry (455)
Last modified by	Henry (455)
Numerical id	4
Author	Henry (455)
Entry type	Theorem
Classification	msc 03E40