Ignatiev proved that the restriction of the ordering <₀ to the letterless fragment of GLP is, indeed, a well-founded ordering of type epsiolon_0+1 (the 1 here comes from falsity). This, essentially, allows to use it as the ordinal notation system for the analysis of PA.

Ignatiev conjectured that the same holds for the whole Lindenbaum algebra of GLP and obtaioned some sufficient conditions, but he did not get the final result.

I do not see any proof-theoretical applications of a possible solution to this problem, so far, but this is a natural question that will shed some additional light on the modal logic properties of GLP. So, it would be good if we new the answer.