  We introduce the logics GLP(\Lambda), a generalization of Japaridze's
polymodal provability logic GLP(\omega) where \Lambda is any linearly ordered
set representing a hierarchy of provability operators of increasing strength.
  We shall provide a reduction of these logics to GLP(\omega) yielding among
other things a finitary proof of the normal form theorem for the variable-free
fragment of GLP(\Lambda) and the decidability of GLP(\Lambda) for recursive
orderings \Lambda. Further, we give a restricted axiomatization of the
variable-free fragment of GLP(\Lambda).

Logic