On the uniqueness of maximal immediate extensions of valued differential fields

摘要

So far there exist just a few results about the uniqueness of maximalimmediate valued differential field extensions and about the relationshipbetween differential-algebraic maximality and differential-henselianity. Weremove here the assumption of monotonicity in these results but replace it withthe assumption that the value group is the union of its convex subgroups offinite (archimedean) rank. We also show the existence and uniqueness ofdifferential-henselizations of asymptotic fields with such a value group.