In this paper, we first introduce and characterize a new and general concept of a credible deviation in which a coalition may not only deviate from a deviant coalition, but may also merge with some residual players. Thus objections are not necessarily nested in the sense of coming from subsets of progressively smaller coalitions. We then motivate and introduce an infinitely farsighted stable set which is not amenable to similar criticisms as a traditional von Neumann-Morgenstern stable set or a Harsanyi stable set. After noting its general properties, we prove existence and characterize infinitely farsighted stable sets for general three-player superadditive characteristic function games with empty or nonempty cores as well as for convex games with any number of players.