Cardinal sequences

István Juhász, William Weiss

In this article we characterize all those sequences of cardinals of length $ \omega_1$ 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 $ \omega_1$ and $ \omega_2$ 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].


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