For any formula formula_26, the class formula_180 equals formula_72 when formula_26 can be rejected and formula_107 when formula_26 can be proven, but formula_26 may also not be decidable at all. In this view, the powerclass of the singleton formula_186, i.e. formula_187 or informally formula_188 and usually denoted by formula_189, is called the truth value algebra. Assuming all formulas are decidable, i.e. assuming formula_3, one can show not only that formula_189 is a set, but more concretely that it is this two-element set. Assuming formula_3 for bounded formulas, Separation lets one demonstrate that any powerclass is a set. Alternatively, full Powerset is equivalent to merely assuming that the class of all subsets of formula_107 forms a set. Full Separation is equivalent to assuming that each subclass of formula_107 is a set.