ریحانه ذوقی‌فرد، محمد گلشنی

پژوهشگاه دانش‌های بنیادی

Abstract. In 1990, Andreas Blass introduced a filter sequence semantic for modal logic and showed that the provability logic GL is complete with respect to the end filter sequence. He also showed that it is consistent that GL is complete with respect to the club filter and that in this case, it's incompleteness is equiconsistent with the existence of a Mahlo cardinal. He asked if it is consistent that GL is complete with respect to the normal filter sequence. In this talk, we answer the above question. Assuming the existence of suitable large cardinals, we show that it is consistent that GL is complete with respect to the normal filter sequence. This is joint work with Reihane Zoghifard.