On collectionwise normality of locally compact, normal spaces

Abstract

We prove that by adjoining supercompact many Cohen or random reals to a model of ZFC set theory, in the resulting model, every normal locally compact space is collectionwise normal. In the same models, countably paracompact, locally compact T 3 {T_3} -spaces are expandable. Local compactness in the above theorems can be weakened to being of point-countable type, a condition that is implied by both Čech-completeness and first countability.