The main result of this paper is the following theorem: a closure space *X* has an 〈*α, δ*, Q〉-regular base of the power
$$\mathfrak{n}$$
iff *X* is *Q*-embeddable in
$$B_{\alpha ,\delta }^\mathfrak{n} $$
It is a generalization of the following theorems:
(i)

Stone representation theorem for distributive lattices (*α* = 0, *δ = ω, Q = ω*),

(ii)

universality of the Alexandroff's cube for *T*_{0}-topological spaces (α = ω, *δ = ∞, Q* = 0),

(iii)

universality of the closure space of filters in the lattice of all subsets for 〈*α, δ*〉-closure spaces (*Q* = 0).

By this theorem we obtain some characterizations of the closure space
$$F_\mathfrak{m} $$
given by the consequence operator for the classical propositional calculus over a formalized language of the zero order with the set of propositional variables of the power
$$\mathfrak{m}$$
. In particular we prove that a countable closure space *X* is embeddable with finite disjunctions preserved into *F*_{ω} iff *X* is a consistent closure space satisfying the compactness theorem and *X* contains a 〈0, ω〉-base consisting of ω-prime sets.

This paper is a continuation of [7], [2] and [3].