Plus ultra

Details Plus ultra Plus ultra

2012-01-05

arxiv.org/abs/1201.1114v2

Mathematics

Logic

Scientific paper

We develop some basic simplicity-theoretic facts for quasi-finitary ultraimaginaries, i.e.\ classes of finite tuples modulo $\emptyset$-invariant equivalence relations, in a supersimple theory. We also show that they are geometrically eliminable in a weak sense: If $e$ is an ultraimaginary definable over a tupe $a$ with $SU(a)<\omega^{\alpha+1}$, then $e$ is eliminable up to rank $<\omega^alpha$. Finally, we show some uniform versions of the weak canonical base property.

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