O-Minimal Fields With Standard Part Map

Let R be an o-minimal field and V a proper convex subring of R with residue field k. Let kind be the expansion of the residue field by the standard parts of definable relations on R. We investigate the definable sets in kind and conditions on (R,V) which imply o-minimality of kind. We also show that if R is o-saturated and V is the convex hull of Q in R, then the sets definable in k ind are exactly the standard parts of the sets definable in ( R,V). Using our description of definable sets in k ind we give a partial answer to a question posed by Hrushovski, Peterzil and Pillay about the existence of measures with a certain invariance property on the lattice of bounded definable sets in Rn.

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

• Marikova, Jana

Contributors dc:contributor

• Henson, C. Ward

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI3337861

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86909