ABSTRACT
This chapter shows that PM + LPC1 is consistent with respect to negation. The theses of PM+LPC1 fall into two classes: those which are wffs of PM, and those which are wffs of LPC1. An axiomatic basis is said to be weakly complete if every valid wff is derivable as a thesis. To say that an axiomatic basis is strongly complete is to say that the addition as an extra axiom of any wff which is not derivable from the original basis would make the system inconsistent. The chapter also shows that the basis for PM +LPC1 is not strongly complete by finding a wff not derivable from it, whose addition to the axiom set would not make the system inconsistent.
