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1 results

  • MODEL COMPLETENESS OF O-MINIMAL FIELDS WITH CONVEX VALUATIONS

  • CLIFTON F. EALY, JANA MAŘÍKOVÁ
  • Journal:
    The Journal of Symbolic Logic / Volume 80 / Issue 1 / March 2015
    Published online by Cambridge University Press:
    13 March 2015, pp. 234-250
    Print publication:
    March 2015

  • 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).