  Countable tightness may be destroyed by countably closed forcing. We
characterize the indestructibility of countable tightness under countably
closed forcing by combinatorial statements similar to the ones Tall used to
characterize indestructibility of the Lindelof property under countably closed
forcing. We consider the behavior of countable tightness in generic extensions
obtained by adding Cohen reals. We show that certain classes of well-studied
topological spaces are indestructibly countably tight. Stronger versions of
countable tightness, including selective versions of separability, are further
explored.
