 This account of algebraizability has been oversimplified for expository purposes in one respect: Blok and Pigozzi (1989) do not require the translation of a formula (what we are calling τ) should yield a single equation, but allow a set of equations, and similarly in the converse direction, τ′(e) is allowed to be a set of formulas. It follows from the present definition, with the single equation/single formula restriction removed, that the formulas in the latter set function collectively as an equivalence-like compound satisfying some further congruence conditions, which in the case of ⊢R can be taken to be ↔. Accordingly, the fact that ⊢R—explained presently—is algebraizable, entails, in view of the “φ ⊣⊢ τ′(τ(φ))” condition, that, loosely speaking, every formula is equivalent to an equivalence. But does this not clash with our finding that ↔ is special in R?