Friedman's 14-th problem.
From Peano's Parlour
Let $T$ be a completion of PA. Let ${\rm Ot}(T)$ be the spectrum of order types of nonstandard models of $T$. In [1] Harvey Friedman asked: Does ${\rm Ot(T)}$ depend on $T$?
Shelah has recently announced that the answer in negative, but there is no paper available yet. See Sh[924] for an interesting effort in the opposite direction.
