Rabin Michael O.. Effective computability of winning strategies. Contributions to the theory of games, Volume III, Annals of Mathematics studies number 39, Princeton University Press, Princeton, New Jersey, 1957, pp. 147–157.

N. D. GAUTAM. The validity of equations of complex algebras. Archiv fiir mathematische Logik und Grundlagenforschung, vol. 3 (1957), pp. 117-124. The multiplication of complexes (subsets) of a given group is defined in a wellknown way, and this definition can be extended in an obvious manner to arbitrary (Birkhoff) algebras. Now consider any equation tx = t2 where both tx and t2 are obtained by the repeated application of the basic operations of an algebra A to a set of variables. We say that tx = t2 is satisfied by A if the sentence obtained from tt = t2 by the universal quantification of the free variables holds in it. This paper settles the problem under what conditions the fact that tx = t2 is satisfied in A entails that it is satisfied also by the algebra of complexes of A. The answer, simple and satisfying, states that this is the case if and only if every variable that occurs in t± = t2 occurs just once both in tx and in t2. Remark. Since in Definition 5 the author defines c-validity for a set of algebras, he should have mentioned that in Theorems 1, 3, 4, c-validity is defined with respect to all algebras for which tt = t2 is defined. ABRAHAM ROBINSON