Affiliation:
1. Department of Mathematics and Statistics McMaster University Hamilton Ontario Canada
Abstract
AbstractWe prove a dichotomy for o‐minimal fields , expanded by a T‐convex valuation ring (where T is the theory of ) and a compatible monomial group. We show that if T is power bounded, then this expansion of is model complete (assuming that T is), it has a distal theory, and the definable sets are geometrically tame. On the other hand, if defines an exponential function, then the natural numbers are externally definable in our expansion, precluding any sort of model‐theoretic tameness.
Funder
National Science Foundation
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