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- W2893707817 abstract "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 theory. In every infinite cardinal, we construct the maximum possible number of pairwise non-isomorphic models of $rbRT_r$; indeed, the models we construct are pairwise non-homeomorphic. We give detailed information about the type spaces of $rbRT_r$. Among other things, we show that the space of $2$-types over the empty set is nonseparable. Also, we characterize the principal types of finite tuples (over the empty set) and use this information to conclude that $rbRT_r$ has no atomic model." @default.
- W2893707817 created "2018-10-05" @default.
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- W2893707817 date "2020-12-28" @default.
- W2893707817 modified "2023-10-01" @default.
- W2893707817 title "Model theory of R-trees" @default.
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- W2893707817 doi "https://doi.org/10.4115/jla.2020.12.3" @default.
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