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MODEL COMPLETENESS OF O-MINIMAL FIELDS WITH CONVEX VALUATIONS

Published online by Cambridge University Press:  13 March 2015

CLIFTON F. EALY  and
JANA MAŘÍKOVÁ
CLIFTON F. EALY
Affiliation:
DEPARTMENT OF MATHEMATICS, WESTERN ILLINOIS UNIVERSITY, MACOMB, IL 61455, USAE-mail:cf-ealy@wiu.eduE-mail:j-marikova@wiu.eduURL: http://www.wiu.edu/users/cfe100/URL: http://www.wiu.edu/users/jm112
JANA MAŘÍKOVÁ
Affiliation:
DEPARTMENT OF MATHEMATICS, WESTERN ILLINOIS UNIVERSITY, MACOMB, IL 61455, USAE-mail:cf-ealy@wiu.eduE-mail:j-marikova@wiu.eduURL: http://www.wiu.edu/users/cfe100/URL: http://www.wiu.edu/users/jm112
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Abstract

We let R be an o-minimal expansion of a field, V a convex subring, and (R0,V0) an elementary substructure of (R,V). Our main result is that (R,V) considered as a structure in a language containing constants for all elements of R0 is model complete relative to quantifier elimination in R, provided that kR (the residue field with structure induced from R) is o-minimal. Along the way we show that o-minimality of kR implies that the sets definable in kR are the same as the sets definable in k with structure induced from (R,V). We also give a criterion for a superstructure of (R,V) being an elementary extension of (R,V).

Keywords

O-minimalconvex valuationsmodel completenessMorley sequencesforking

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Type
Articles
Information
The Journal of Symbolic Logic , Volume 80 , Issue 1 , March 2015 , pp. 234 - 250
Copyright
Copyright © The Association for Symbolic Logic 2015 

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