The countable rational Urysohn ultrametric space U is the Fraïssé limit of finite two-sorted ultrametric spaces under dc-embeddings and is dc-universal for all countable ultrametric spaces, with its completion universal for separable ones.
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Universal homogeneous two-sorted ultrametric spaces
The countable rational Urysohn ultrametric space U is the Fraïssé limit of finite two-sorted ultrametric spaces under dc-embeddings and is dc-universal for all countable ultrametric spaces, with its completion universal for separable ones.