Scattered spaces from weak diamonds
Parametrized ♦-principles introduced in  associated to the cardinal invariants s and b are used to construct (1) a family of sequentially compact spaces whose product is not countably compact — an example for the Scarborough–Stone problem, (2) a Jakovlev space, and (3) a compact sequential space of sequential order ω1. All spaces constructed are scattered, locally compact and of size ω1.
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