Using methods from nonstandard analysis, we will discuss which metric spaces
can be realized as asymptotic cones. Applying the results we will find in the
context of groups, we will prove that a group with "a few" separable asymptotic
cones is virtually nilpotent, and we will classify the real trees appearing as
asymptotic cones of (not necessarily hyperbolic) groups.Comment: The hypothesis of Theorem 1.2 had to be strengthene