On the classification of propositional provability logics

The general notion of a modal propositional provability logic was introduced by S. N. Artëmov (1979) and A. Visser (1984). In this paper it is proved that the four infinite series of provability logics known at the present time – $\operatorname{GL}_\alpha$, $\operatorname{GL}_\beta^-$, $S_\beta$, and $D_\beta$ ($\alpha,\beta\subseteq\omega$, $\omega\setminus\beta$ finite) – include all such logics.
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