Model Theory of Differentially Closed Fields With Several Commuting Derivations

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Suer, Sonat

Contributors dc:contributor

• Pillay, Anand

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI3290394

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86891