Rectangular axioms, perfect set properties and decomposition

J.,Brendle, P.,Larson, S.,TodorceviŠ

We consider three combinatorial topics appearing in G{o}del's manuscript emph{Some considerations leading to the probable conclusion that the true power of the continuum is $\aleph_{2}$}. These statements concern rectangular functions, perfect set properties, and covering properties of sets of reals. We consider these statements in light of more recent work on the set theory of the reals.