Universal Knowledge-Belief Structures

In this paper, we provide a notion of structure preserving maps (i.e. knowledge–belief morphisms) between knowledge–belief spaces. Then we show that—under the condition that the knowledge operators of the players in a knowledge–belief space operate only on measurable subsets of the space—there is a unique (up to isomorphism) universal knowledge–belief space to which every knowledge–belief space can be mapped by a unique knowledge–belief morphism.