Compact spaces, elementary submodels, and the countable chain condition, II

Given a space (X, T) in an elementary submodel of H(theta), define X-M to be X boolean AND M with the topology generated by {U boolean AND M: U is an element of T boolean AND M). It is established that if X-M is compact and satisfies the countable chain condition, while X is not scattered and has cardinality less than the first inaccessible cardinal, then X = X-M. If the character of X-M is a member of M, then "inaccessible" may be replaced by "1-extendible". (C) 2005 Elsevier B.V. All rights reserved.