Geodesic
On the classification of propositional provability logics
Izvestiya. Mathematics , Tome 35 (1990) no. 2, pp. 247-275

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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. Bibliography: 14 titles. 
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     author = {L. D. Beklemishev},
     title = {On the classification of propositional provability logics},
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L. D. Beklemishev. On the classification of propositional provability logics. Izvestiya. Mathematics , Tome 35 (1990) no. 2, pp. 247-275. http://geodesic.mathdoc.fr/item/IM2_1990_35_2_a0/