This is really a note to Wajsberg's [4].

In [3] J. C. C. McKinsey proved the following two completeness theorems: (1) theorem 6: If A is a wff of S2 with just r (proper or improper) sub-wffs, then A is provable in S2 iff A is satisfied by every normal S2-matrix with no more than 22r+1 elements; (2) theorem 13: if A is a wff of S4 with just r sub-wffs, then A is provable in S4 iff A is satisfied by every normal S4-matrix with no more than 22r elements. Now, a similar theorem has not been explicitly formulated for S5, even though a similar, even simpler, theorem has been almost at hand since Wajsberg's [4] was published in 1933, namely:

Theorem. If A is a wff of S5 with just n propositional variables, then A is provable in S5 iff A is satisfied by a normal SS-matrix with 22n elements.