How canonical is the canonical model? A comment on aumann's interactive epistemology

Aumann (1989) argued that the natural partitions on the space of all maximally consistent sets of formulas in multi-player S5 logic are necessarily "commonly known" by the players. We show, however, that there are many other sets of partitions on this space that conform with the formulas that build the states - as many as there are subsets of the continuum! Thus, assuming a set of partitions on this space is "common knowledge" is an informal but meaningful meta-assumption.