1. L. D. Beklemishev, “Provability algebras and proof-theoretic ordinals, I,” Ann. Pure Appl. Logic 128(1–3), 103–123 (2004).
2. G. K. Dzhaparidze, Modal-Logic Tools for Studying Provability, Candidate’s Dissertation in Philosophy (Moscow State Univ., Moscow, 1986).
3. K. N. Ignatiev, “On strong provability predicates and the associated modal logics,” J. Symbolic Logic 58(1), 249–290 (1993).
4. L. D. Beklemishev, “The worm principle,” in Lecture Notes in Logic, Vol. 27: Logic Colloquium’ 02 (Assoc. Symbol. Logic, La Jolla, Ca., 2006), pp. 75–95.
5. I. Shapirovsky, “PSPACE-decidability of Japaridze’s polymodal logic,” in Advances in Modal Logic (College Publ., London, 2008), Vol. 7, pp. 289–304.