István Juhász, William Weiss
In this article we characterize all those sequences of cardinals of length which are cardinal sequences of some (locally) compact scattered space (or, equivalently, a superatomic boolean algebra). This extends the similar results from [LG] for such sequences of countable length. For ordinals between and we can only give a sufficient condition for a sequence of that length to be a cardinal sequence of a compact scattered space. This condition is, arguably, the most one can expect in ZFC. In any case, ours is a significant extension of the sufficient conditions given in [M] and [B].