 Is many-sorted logic a proper (or strict) extension of first-order logic? Lindström (1969) proves that first-order logic is characterizable as the strongest logic to possess simultaneously Compactness and Löwenheim-Skolem properties. Moreover, first-order logic is the strongest logic where Löwenheim-Skolem holds and its set of valid sentences is recursively enumerable. Therefore, many-sorted logic cannot be considered as a proper extension of first-order logic.