An invariant way to see the particular equivalence discussed is to note that the topos of presheaves on the category of finite sets is the classifying topos for p-algebras for any given p > 1. That is because any non-empty set is a retract of a finite power of p and because left-exactness is equivalent to preserving finite products in this particular case. This representation suggests a different interpretation from the usual "truth of properties" point of view concerning the essential content of Boolean algebra. Namely, it concerns finite partitions of a hypothetical whole and shuffling of these induced by arbitrary maps between the index sets for the partitions, nothing more. Coordinatizing the above shuffling of partitions using p = 3 has some advantages over p = 2, namely, the unary operations of the theory suffice to characterize ultrafilters, i.e. to insure that perceived points of a finite set are actually there; more formally, the contravariant functor represented by 3 from finite sets to M-sets is full where M is the 27-element monoid of these unary operations. ************************************************************ F. William Lawvere Mathematics Department, State University of New York 244 Mathematics Building, Buffalo, N.Y. 14260-2900 USA Tel. 716-645-6284 HOMEPAGE: http://www.acsu.buffalo.edu/~wlawvere ************************************************************