In this paper, we introduce a concept of a farsighted stable set for a partition function game and interpret the union of all farsighted stable sets as the core of the game, to be called the strongcore, which reduces to the traditional core if the worth of every coalition is independent of the partition to which it belongs and the game is adequately represented by a characteristic function. We show that every farsighted stable set for a partition function game, like a characteristic function game, contains just a single feasible payoff vector, and the strong-core (i.e. the union of all farsighted stable sets) is nicely related to two previous core concepts for partition function games. Finally, we justify the farsighted stable sets also as a non-cooperative solution concept by showing that every farsighted stable set can be supported as an equilibrium outcome of an infinitely repeated game.