Plus ultra

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 $SU(a)<ω^{α+1}$, then $e$ is eliminable up to rank $<ω^α$. Finally, we prove some uniform versions of the weak canonical base property.

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