Locally-generic Boolean algebras and cardinal sequences. (Q1771919)

Given a sequence of cardinals \(\theta \) of length less than \(\omega _{2}\), with each cardinal in the sequence being either \(\omega \) or \(\omega _{1}\), the author constructs a \(\theta \)-poset which, with a natural topology, becomes a locally compact Hausdorff scattered space with cardinal sequence \(\theta \). The algebra of the clopen subsets of its one-point compactification yields a superatomic Boolean algebra with \(\theta \) as its cardinal sequence. The posets are shown to be locally generic, i.e.\ they are constructed generically over countable sets.