It is known that the notion of the absolute ego of consciousness was described by Husserl in terms of the constitution and the continuous flow of internal time. It is remarkable that gradually Husserl tended to think of it not only in terms of temporality but in its generality as the source of all temporality, "reached" through a radical phenomenological reduction. We take into account the stages by which he was led to the impredicativity of the absolute ego of consciousness and try to demonstrate how this is reflected in the axiomatization of continuum in certain non-Cantorian mathematical theories to the extent that undertake a formalisation beyond natural intuition. We also review those theories' approach to classical mathematical notions as this approach is more close to Husserl's shift of the horizon idea.