  Iterated admissibility (IA) can be seen as exhibiting a minimal criterion of
rationality in games. In order to make this intuition more precise, the
epistemic characterization of this game-theoretic solution has been actively
investigated in recent times: it has been shown that strategies surviving m+1
rounds of iterated admissibility may be identified as those that are obtained
under a condition called rationality and m assumption of rationality (RmAR) in
complete lexicographic type structures. On the other hand, it has been shown
that its limit condition, $R\infty AR$, might not be satisfied by any state in
the epistemic structure, if the class of types is complete and the types are
continuous. In this paper we introduce a weaker notion of completeness which is
nonetheless sufficient to characterize IA in a highly general way as the class
of strategies that indeed satisfy $R\infty AR$. The key methodological
innovation involves defining a new notion of generic types and employing these
in conjunction with Cohen's technique of forcing.
