  Brandenburger, Friedenberg, and Keisler provide an epistemic characterization
of iterated admissibility (i.e., iterated deletion of weakly dominated
strategies) where uncertainty is represented using LPSs (lexicographic
probability sequences). Their characterization holds in a rich structure called
a complete structure, where all types are possible. Here, a logical
charaacterization of iterated admisibility is given that involves only standard
probability and holds in all structures, not just complete structures. A
stronger notion of strong admissibility is then defined. Roughly speaking,
strong admissibility is meant to capture the intuition that "all the agent
knows" is that the other agents satisfy the appropriate rationality
assumptions. Strong admissibility makes it possible to relate admissibility,
canonical structures (as typically considered in completeness proofs in modal
logic), complete structures, and the notion of ``all I know''.
