Complete separation in the random and Cohen models

It is shown that in the model obtained by adding kappa many random reals, where kappa is a supercompact cardinal, every C*-embedded subset of a first countable space (even with character smaller than kappa) is C-embedded. It is also proved that if two ground model sets are completely separated after adding a random real then they were completely separated originally but CH implies that the Cohen poset does not have this property. (C) 2011 Elsevier B.V. All rights reserved.