KNOWLEDGE SPACES WITH ARBITRARILY HIGH RANK

The class of probabilistic belief spaces (Harsanyi, 1967-68, Man. Sci. , 14, 159-182, 320-324, 486-502) contains a universal space, into whic h every other belief space can be mapped in a unique way by a belief m orphism. We show that there is no analogous universal space in the cla ss of knowledge spaces. To show this we define the rank of a knowledge space, which is the ordinality of the most complicated descriptions o f knowledge in the space, We then show that a knowledge space can be m apped by a knowledge morphism only to spaces of higher or equal rank. We construct knowledge spaces for arbitrarily high rank, demonstrating that there is no universal space. (C) 1998 Academic Press.