  We study transfinite extensions of Japaridze's provability logic GLP and the
well-founded relations that naturally occur within them. Every ordinal induces
a partial order over the class of "words," which are iterated consistency
statements expressible within GLP. Well-ordered restrictions of these partial
orders have been studied previously; in this paper we consider the unrestricted
partial orders, which are no longer linear but remain well-founded. These
unrestricted partial orders bear important repercussions on modal semantics for
GLP and on Turing progressions.
