Specifying nodes as sets of choices

Osborne and Rubinstein (1994) specify each node in a game tree as a sequence of actions. It is well-known that such actions can be replaced by choices (i.e. agent-specific actions) without loss of generality. I find that this sequential formulation is redundant in the sense that nodes can be equivalently specified as sets of choices. The only cost of doing so is to rule out absent-mindedness. My analysis encompasses both ordered and unordered information sets and both finite and infinite horizons. (This specification of nodes as sets of choices differs from the literature's specification of nodes as sets of outcomes.)