  We determine the general conditions for the existence of Godel, Einstein
static, and de Sitter universes in gravity theories derived from a Lagrangian
that is an arbitrary function of the scalar curvature and Ricci and Riemann
curvature invariants. Explicit expressions for the solutions are found in terms
of the parameters defining the Lagrangian. We also determine the conditions on
the Lagrangian of the theory under which time-travel is allowed in the Godel
universes.
