One dimensional structures in o-minimal theories
classification
🧮 math.LO
keywords
dimensionalo-minimalstructurescurvesdefinabledevelopintersectionlocally
read the original abstract
We prove the Zil'ber Trichotomy Principle for all 1-dimensional structures which are definable in o-minimal ones. In particular, we show that any stable 1-dimensional structure is necessarily locally modular. The main tool is a theory for intersection of curves which we develop.
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