  We prove strong cosmic censorship for T^2-symmetric cosmological spacetimes
(with spatial topology T^3 and vanishing cosmological constant Lambda) with
collisionless matter. Gowdy symmetric spacetimes constitute a special case. The
formulation of the conjecture is in terms of generic C^2-inextendibility of the
metric. Our argument exploits a rigidity property of Cauchy horizons, inherited
from Killing fields.
