ABSTRACT
Theorem 10.1, therefore, establishes something that theorem 6.7 does not. Does this mean that it is stronger than theorem 6.7, that it proves all that that theorem proves and more besides? If it did, that would indeed be gratifying, since the proof of theorem 10.1 is a great deal simpler than a completeness proof by canonical models. Unfortunately, however, there is no short cut to a completeness proof by this method. Certainly, if T is characterized by any class of frames at all, then it will be characterized by the class of all frames for T, and then corollary 10.2 assures us that in that case it is characterized by the class of all reflexive frames. But the hypothesis here is that T is characterized by some class of frames; and that is something that corollary 10.2 does not tell us, and which we need a separate proof to establish.
