  We give an example of a definable quotient in an o-minimal structure which
cannot be eliminated over any set of parameters, giving a negative answer to a
question of Eleftheriou, Peterzil, and Ramakrishnan. Equivalently, there is an
o-minimal structure M whose elementary diagram does not eliminate imaginaries.
We also give a positive answer to a related question, showing that any
imaginary in an o-minimal structure is interdefinable over an independent set
of parameters with a tuple of real elements. This can be interpreted as saying
that interpretable sets look "locally" like definable sets, in a sense which
can be made precise.
