On the Incompleteness of a Descending Chain of Extensions of Implicational S5

Abstract

C5.w is obtained by adding, schematically, to the strict-implicational fragment C 5 of S 5 the axiom ((p -. ) q ) + ( q ' p ) ) + ( q ' p ) . This paper presents a fully general proof that neither C5.w nor any of a descending chain of its extensions is complete with respect to any class of frames, correcting the garbled details of a version skcched in an earlier paper (same Zeitschrift 31 (1985), 201-208). MSC: 03B45.