Kohlberg and Mertens defined tentatively a set-valued solution concept called stability for games with finite numbers of pure strategies that satisfies admissibility, invariance and forward induction, but a counterexample showed that it need not satisfy backward induction; viz. the set might not include a sequential equilibrium.
Backward Induction and Forward Induction: A stable set includes a proper equilibrium of the normal form of the game that induces a quasi-perfect and sequential equilibrium in every extensive-form game with perfect recall that has the same normal form.