Strong zero-dimensionality of products of ordinals. (Q1403810)

After some set-theoretical preparation (including a generalized pressing down lemma for \(n\)-tuples of ordinals and its consequences) the authors prove that every finite product of subspaces of ordinals is strongly zero-dimensional. Although every subspace of such a product is zero-dimensional, it need not be strongly zero-dimensional: \(2^\omega\) is the minimum cardinal such that \((\omega+1)\times 2^\omega\) is not hereditarily strongly zero-dimensional (in fact, it contains subspaces of any finite dimension).