A consistency result on long cardinal sequences

Abstract

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

Minor revision. arXiv admin note: text overlap with arXiv:0712.0584