Model theory of R-trees

@article{Carlisle2020ModelTO,
  title={Model theory of R-trees},
  author={Sylvia Carlisle and C. Ward Henson},
  journal={J. Log. Anal.},
  year={2020},
  volume={12}
}
We show the theory of pointed $\R$-trees with radius at most $r$ is axiomatizable in a suitable continuous signature. We identify the model companion $\rbRT_r$ of this theory and study its properties. In particular, the model companion is complete and has quantifier elimination; it is stable but not superstable. We identify its independence relation and find built-in canonical bases for non-algebraic types. Among the models of $\rbRT_r$ are $\R$-trees that arise naturally in geometric group… 
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