Let L be some classical languagee and let ⊢ be an appropriate classical consequence relation.
If Γ is a set of sentences in L, Γ⊢ denotes the closure of Γ under
⊢.
A covering of Γ is a set {Γi| i ∈ I} of classical consistent sets of sentences
such that Γ = S
i∈I Γi
. If C = {Γi
| i ∈ I} is a covering of Γ, a permeability
relation ρ on C is a map from I × I to sets of sentences of L. If i0 ∈ I, hC, ρ, i0i
is called a C & P structure on Γ.
If P = hC, ρ, i0i is a C & P structure on Γ and A is a sentence in the language
under consideration, then