Relationship among universal type space, Aumann's semantic knowledge model and Samet's syntactic knowledge model
There is no "universal Aumann model", as shown in Heifetz &amp; Samet, GEB 1998, "Knowledge Spaces with Arbitrarily High Rank
", even though there is a universal type space.

On a less technical level, Aumanns model does not allow for wrong beliefs. A generalization, so called Kripke structures, do however.