  We define a reasonably well-behaved class of ultraimaginaries, i.e.\ classes
modulo invariant equivalence relations, called {\em tame}, and establish some
basic simplicity-theoretic facts. We also show feeble elimination of
supersimple ultraimaginaries: If $e$ is an ultraimaginary definable over a
tuple $a$ with $SU(a)<\omega^{\alpha+1}$, then $e$ is eliminable up to rank
$<\omega^\alpha$. Finally, we prove some uniform versions of the weak canonical
base property.

Logic