Corrigendum

In my note (S. R. Kogalovskii, “On the relationship between finitely projective and finitely reduction classes of models”), published in Doklady Akademii Nauk, vol. 155, no. 6, 1964, Theorem 3 is incorrect and should be replaced by the following theorem, which is easily proved with the aid of the Craig–Vaught theorem on recursively axiomatizable classes of infinite models:

Theorem 3. For every recursively enumerable set \(J\) there exists a recursively axiomatizable, and hence finitely reduction, class of models whose finite spectrum is a complement of \(J\).

It is easy to see that Theorem 4, which is the principal result of the note, follows directly from the last theorem and Theorem 2.

S. Kogalovskii