"Beklemishev et al. (1999)); the logic of explicit proofs (see Artëmov (2001)); applications of provability logic in proof theory (see Beklemishev bimodal provability logics with provability operators for different theories (see Beklemishev (1994, 1996)); and provability algebras, also called diagonalizable algebras or Magari algebras (see Shavrukov (1993, 1997))."