 In the same way as the fully selfextensional logics are the selfextensional logic systems that enjoy the property that in every one of their full g-models the abstract version of the characteristic property defining selfextensionally holds, the fully Fregean logics are the Fregean logics that in every one of their full g-models  the abstract version of the characteristic property defining being Fregean holds. The next can be taken as the best understandable definition.