Pc. Eklof et S. Shelah, ON A CONJECTURE REGARDING NONSTANDARD UNISERIAL MODULES, Transactions of the American Mathematical Society, 340(1), 1993, pp. 337-351
We consider the question of which valuation domains (of cardinality N1
) have nonstandard uniserial modules. We show that a criterion conject
ured by Osofsky is independent of ZFC + GCH .