## Global sub-$\C$-sets

Finally, we get to Step 3 of the proof of this theorem: establishing a theorem of the complement for the “right” collection of existentially definable sets. We start with a few exercises. Exercises Let $\tau_n:\RR^n \into (-1,1)^n$ be the semialgebraic diffeomorphism defined here. Show that, for every semialgebraic set $A \subseteq \RR^n$, the set $\tau_n(A)$…