One dimensional structures in o-minimal theories

2007/02/25 by Hasson, Assaf, Onshuus, Alf, Peterzil, Ya'acov
#03C45 #03C64 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.math/0702748

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.

Related

• Unstable structures definable in o-minimal theories
• Strongly minimal groups in o-minimal structures
• An introduction to o-minimal structures
• Restricted trichotomy in higher dimensions
• Restricted Trichotomy in Characteristic Zero