 What other open questions of set theory could be solved by Gödel’s method? Gödel himself noted some consequences. They are related to so called projective sets of real numbers and finite sequences of real numbers. The simplest projective sets are the closed sets, also called Π10-sets. A set is Σ1n+1 if it is the projection of a Π1n-subset of the real plane. A set is Δ1n+1 if it and its complement are Σ1n+1. Gödel observed that there is both a non-Lebesgue measurable Δ12-set and an uncountable Π11-set without a perfect subset in L. (A set of reals is perfect if it is closed, non-empty, and has no isolated points. Such sets have the size of the continuum.) Gödel gave a sketch of the proof in the 1951 second printing of Gödel 1940.