An error in a proof in: Boolean algebras with operators. I (Q1652869)

The theorem in question is Theorem 5. in [\textit{B. Jónsson} and \textit{A. Tarski}, Am. J. Math. 73, 891--939 (1951; Zbl 0045.31505)]. The theorem gives a necessary and sufficient condition for a function \(f\) defined on \(A\) (or on \(A^{2})\), mapping to \(A\) to be completely additive. The proposition of the theorem is correct. The authors present a correct proof, pointing out the error in the original proof.