## Cardinal sequences

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].

#### Bibliography

B
J. Bagaria, Locally generic Boolean algebras and cardinal sequences, Alg. Univ. 47 (2002), pp. 283 - 302.

LG
R. La Grange, Concerning the cardinal sequence of a Boolean algebra, Alg. Univ. 7 (1977), pp. 307 - 313.

M
J. C. Martinez, A consistency result on thin-tall superatomic Boolean algebras, Proc. AMS 115 (1992), pp. 473 - 477.