University of Illinois Urbana-Champaign

Model Theory of Differentially Closed Fields With Several Commuting Derivations

Suer, Sonat

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https://hdl.handle.net/2142/86891

Description

Title
Model Theory of Differentially Closed Fields With Several Commuting Derivations
Author(s)
Suer, Sonat
Issue Date
2007
Doctoral Committee Chair(s)
Pillay, Anand
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
In this thesis we deal with the model theory of differentially closed fields of characteristic zero with several commuting derivations. The questions we consider belong to the area of geometric stability theory. 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. Then we show that the generic type of the heat variety, which is one of these new types, is locally modular. So, unlike the case of ordinary differential fields, the additive group of a partial differential field has locally modular subgroups. We also classify the subgroups of the additive group of Lascar rank omega with differential-type 1 which are nonorthogonal to fields.
Graduation Semester
2007
Type of Resource
text
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http://hdl.handle.net/2142/86891

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