The conditions are logically equivalent. Unfortunately, I don’t see a way to show this without using the partition poset terminology that I intended to avoid. Nonetheless, if you unpack the definition of “common knowledge” in Aumann’s paper, it is equivalent to what I gave. (ETA: I give the unpacking in this comment.)
The conditions are logically equivalent. Unfortunately, I don’t see a way to show this without using the partition poset terminology that I intended to avoid. Nonetheless, if you unpack the definition of “common knowledge” in Aumann’s paper, it is equivalent to what I gave. (ETA: I give the unpacking in this comment.)