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https://hdl.handle.net/2142/86909
Description
Title
O-Minimal Fields With Standard Part Map
Author(s)
Marikova, Jana
Issue Date
2008
Doctoral Committee Chair(s)
Henson, C. Ward
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
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.
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