On the universal partition theorem for 4-polytopes (Q1389169)

Every semialgebraic stratification of \(\mathbb{R}^n\) (defined over \(\mathbb{Z})\) is ,``stably equivalent'' to the family of realization spaces of an effectively computable set of \(4\)-dimensional polytopes. This ``universal partition theorem for \(4\)-dimensional polytopes'' was first established by \textit{J. Richter-Gebert} [see: `Realization spaces of polytopes', Springer LVM Vol. 1643 (1996; Zbl 0866.52009)] who also provided the ``right'' concept of stable equivalence. The new (mostly independent) development and proof of the universal partition theorem for \(4\)-po1ytopes by H. Günzel has several new elements and components. In particular, it provides a substantially more restrictive normal form for the straight-line programs that compute semialgebraic sets/families; furthermore, the ``von Staudt polytopes'' introduced here give a very compact encoding of such normal forms into the combinatorics of \(4\)-polytopes.