We consider first order modal logic C firstly defined by Carnap in “Meaning and Necessity” [1]. We prove elimination of nested modalities for this logic, which gives additionally the Skolem-Löwenheim theorem for C. We also evaluate the degree of unsolvability for C, by showing that it is exactly 0′. We compare this logic with the logics of Henkin quantifiers, Σ11 logic, and SO. We also shortly discuss properties of the logic C in finite models.