this is clearly isomorphic to D1&…&Dm, where Di=(Bi,F,⋆i), where b⋆if=b⋆f. Thus, C’s agent can observe V according to the nonconstructive additive definition of observables.
I think this is only true if VB partitions W, or, equivalently, if vB is surjective. This isn’t shown in the proof. Is it supposed to be obvious?
EDIT: may be able to fix this by assigning any s∈V that is not in VB to the frame ⊤ so it is harmless in the product of Dis—I will try this.
I think this is only true if VB partitions W, or, equivalently, if vB is surjective. This isn’t shown in the proof. Is it supposed to be obvious?
EDIT: may be able to fix this by assigning any s∈V that is not in VB to the frame ⊤ so it is harmless in the product of Dis—I will try this.