mean a characterization which refers only to the metric structure of that space but not its linear structure. In 1976 Ribe [@Ri] showed that two Banach spaces, which are uniformly homeomorphic, have uniformly linearly isomorphic finite-dimensional subspaces. In particular this means that the finite dimensional or [*local*]{} properties of a Banach space are determined by its metric structure. Based on this result Bourgain [@Bo] suggested the “Ribe Program”, which asks to find metric descriptions of finite-dimensional invariants of Banach spaces. In [@Bo] he proved the following characterization of super reflexivity: a Banach space $X$ is super reflexive if and only if the binary trees $B_n$ of length at most $n$, $n\in{\mathbb{N}}$, endowed with their graph metric, are not uniformly bi-Lipschitzly embedded into $X$. A binary tree of length at most $n$, is the set $B_n=\bigcup_{k=0}^n\{-1,1\}^k$, with the [*graph* ]{} or [*shortest path metric*]{} $d(\sigma,\sigma')=i+j  -2\max\{ t\ge 0: \sigma_s=\sigma'_s: s=1,2,\ldots,t\} $, for $\sigma=(\sigma_s)_{s=1}^i\not=\sigma'=(\sigma_s')_{s=1}^j$ in $\bigcup_{k=0}^n\{-1,1\}^k$. A new and shorter proof of this result was recently obtained by Kloeckner in [@Kl]. In [@Ba1] Baudier extended this result and proved that a Banach space $X$ is super reflexive, if and only if the infinite binary tree $B_\infty=\bigcup_{n=0}^\infty \{-1,1\}^n$ (with the graph distance) does 