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Reports on Mathematical Logic

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No. 43

Tomasz KOWALSKI and John SLANEY

A Finite Fragment of S3
A b s t r a c t. It is shown that the pure (strict) implication fragment of the modal
logic [3] (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 [3], in two variables has infinitely many non-equivalent
formulae.

College of Computer Science and Engineering,
Australian National University,
Canberra, 0200 ACT, Australia

tomasz.kowalski,john.slaney@anu.edu.au

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