Common theories

By a theory we mean a subset of propositions that is closed under consequences and conjunctions. When the set of all propositions is a Boolean algebra, theories are filters in this algebra. When there are several theorists, they can also have theories about what theories the other theorists subscribe to. We construct a set of theories which is complete in the sense that it contains all theories about the states of nature and about the set of theories of other agents. This is accomplished by building a complete belief model, where agents' beliefs are modeled by filters. This model is also canonical, terminal and universal.