A lifting theorem on forcing LCS spaces

Lajos Soukup

Denote by $ \mathcal {THIN}(\alpha)$ the statement that there is an LCS space of height $ {\alpha}$ and width $ {\omega}$. We prove, for each regular cardinal $ {\kappa}$, that if there is a ``natural'' c.c.c poset $ P$ such that $ \mathcal {THIN}(\kappa)$ holds in $ V^P$ then there is a ``natural'' c.c.c poset $ Q$ as well such that $ \mathcal {THIN}(\delta)$ holds in $ V^Q$ for each $ {\delta}<{\kappa}^+$.

Key words and phrases: locally compact scattered space, superatomic Boolean algebra, cardinal sequence, lifting theorem

2000 Mathematics Subject Classification: 54A25, 06E05, 54G12, 03E20

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