Indestructible properties of S- and L-spaces

Building on a method of Abraham and Todorčevič we prove a preservation theorem on certain properties under c.c.c. forcings. Applying this result we show that (1) an uncountable, first countable, 0-dimensional space containing only countable and co-countable open subspaces, and (2) S- and L-groups can exist under Martinʹs Axiom.