# 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}
}```
• Published 29 September 2018
• Computer Science, Mathematics
• J. Log. Anal.
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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