# Completeness theorem for QML. A doubt about the relation R in the canonical model. (constant domain)

I dont understand this script:

wRv iff □−w ⊆ v, where

w is a word of W, that is an Lc-saturated set (maximal consistent with the ∀-property, (C is the set of constants that we use to amply the set of formula we have at the start)

and □−w is {A : □A ∈ w}.

I dont get this notation. □−w is the set of all the □A that ∈ w??

If this is correct, why □−w should be a subset of v? Not should be the case that □−w is the set of all the □A that ∈ w, but without the modal operator □?

In this case i can understand why and seems correct: if □A ∈ w so A ∈ v, and □−w is the set of all the formula □A minus the operator □.

I am reading wrong the set notation or i am not understanding the rest?

Thank you.

• What you don't understand since you already explicitly and correctly understood that 'In this case i can understand why and seems correct: if □A ∈ w so A ∈ v, and □−w is the set of all the formula □A minus the operator □.'? Nov 4, 2023 at 21:36