Under set-theoretic hypotheses, it is proved by Magidor and Malitz that logic with the Magidor-Malitz quantifier in the Ki -interpretation is recursively axiomatizable. It is shown here, under no additional settheoretic hypotheses, that this logic cannot be axiomatized by finitely many schemata. Magidor and Malitz [2] introduced the ^-variable-binding quantifiers Q. The language L(Q") is formed...