O-minimal fields with standard part map

2009/01/15 by Maříková, Jana
#03C64 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.0901.2337

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 → 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).

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