On subgroups of the additive group in differentially closed fields
In this paper we deal with the model theory of differentially closed fields of characteristic zero with finitely many commuting derivations. First we observe that the only known lower bound for the Lascar rank of types in differentially closed fields, announced in a paper of McGrail, is false. This gives us a new class of regular types which are orthogonal to fields. Then we classify the subgroups of the additive group of Lascar rank omega with differential-type 1 which are nonorthogonal to fields. The last parts consist of an analaysis of the quotients of the heat variety. We show that the generic type of such a quotient is locally modular. Finally, we answer a question of Phylliss Cassidy about the existence of certain Jordan—Hölder type series in the negative.
Permanent link to this document: http://projecteuclid.org/euclid.jsl/1333566628
Digital Object Identifier: doi:10.2178/jsl/1333566628
Zentralblatt MATH identifier: 06047767
Mathematical Reviews number (MathSciNet): MR2963012