Tomasz KOWALSKI and John SLANEY
A b s t r a c t. It is shown that the pure (strict) implication fragment of the modal logic  (R. K. Meyer, "RI - the bounds of finitude", Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik 16 (1970), pp. 385--387) has finitely many non-equivalent formulae in one variable. The exact number of such formulae is not known. We show that this finiteness result is the best possible, since the analogous fragment of S4, and therefore of , in two variables has infinitely many non-equivalent formulae.
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