On the cardinality and weight spectra of compact spaces, II

by Juhasz and Shelah. [JuSh:612]
Fundamenta Math, 1998
Let B(kappa, lambda) be the subalgebra of P (kappa) generated by [kappa]^{<= lambda} . It is shown that if B is any homomorphic image of B(kappa, lambda) then either |B|< 2^lambda or |B|=|B|^lambda, moreover if X is the Stone space of B then either |X| <= 2^{2^lambda} or |X|=|B|=|B|^lambda . This implies the existence of 0-dimensional compact T_2 spaces whose cardinality and weight spectra omit lots of singular cardinals of ``small'' cofinality.

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