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On subgroups of the additive group in differentially closed fields

Published online by Cambridge University Press:  12 March 2014

Sonat Süer
Sonat Süer*
Affiliation:
Department of Mathematics, Istanbul Bilgi University, Kurtulus Deresi Caddesi No: 47, 34440 Dolapdere, Turkey, E-mail: sonat.suer@bilgi.edu.tr
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Abstract

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 analysis 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.

Keywords

Differential algebrageometric stability theoryregular typeslocal modularity
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 77 , Issue 2 , June 2012 , pp. 369 - 391
Copyright
Copyright © Association for Symbolic Logic 2012

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