Let C <img border=0 width=22 height=17 src="http://fbpe/img/cubo/v13n2/art03-01.jpg" alt="Descripción: Descripción: http://fbpe/img/cubo/v13n2/art03-01.jpg">Reg be a non-empty class (of regular cardinals). Then the logic <img border=0 width=44 height=25 src="http://fbpe/img/cubo/v13n2/art03-02.jpg" alt="Descripción: Descripción: http://fbpe/img/cubo/v13n2/art03-02.jpg">has additional nice properties: it has the homogeneous model existence property.