Plus ultra

Abstract

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.