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Preprint Number 167
167. Jana Maříková O-minimal fields with standard part map Submission date: 24 January 2009. Abstract: Let R be an o-minimal field and V a proper convex subring with residue field k and standard part (residue) map st: V \to k. Let k_{ind} be the expansion of k by the standard parts of the definable relations in R. We investigate the definable sets in k_{ind} and conditions on (R,V) which imply o-minimality of k_{ind}. We also show that if R is omega-saturated and V is the convex hull of the rationals in R, then the sets definable in k_{ind} are exactly the standard parts of the sets definable in (R,V). Mathematics Subject Classification: 03C64 Keywords and phrases: |

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