For any regular cardinal κ and ordinal $\eta <{\kappa }^{++}$ it is consistent that $2^{\kappa }$ is as large as you wish, and every function $f:\eta ⟶[\kappa ,2^{\kappa }]\cap Card$ with $f(\alpha )=\kappa$ for $cf(\alpha )<\kappa$ is the cardinal sequence of some locally compact scattered space.

中文翻译：

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长基数序列的一致性结果

对于任何正则基数κ和序数$\eta <{\kappa }^{++}$ 一致的是 $2^{\kappa }$ 大如你所愿，每一个功能 $F：\eta ⟶[\kappa ,2^{\kappa }]\cap C\mathrm{一种}rd$ 和 $F(\alpha )=\kappa$ 为了 $CF(\alpha )<\kappa$ 是一些局部紧致分散空间的基序。