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Coevents as Beables

Sorkin's coevents can be thought of as the `beables' of a quantum histories theory; in this paper we study the 'logical' implications of taking this claim at face value, constructing a propositional lattice for the space of coevents applicable to a given histories theory and comparing it to the more traditional propositional lattice of events. In particular we focus on multiplicative coevents, and find that the precise nature of their anhomomorphism leads to a particularly simple relationship between the two propositional lattices. Finally, we notice that our constructions contain elements intuitively similar to topos nations of truth values and use this to suggest a means of applying Isham's topos theoretic constructions to multiplicative coevents.