O-Minimal Fields With Standard Part Map

59 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2008.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.U of I OnlyRestricted to the U of I community idenfinitely during batch ingest of legacy ETD