Denote by the statement that there is an LCS space of height and width . We prove, for each regular cardinal , that if there is a ``natural'' c.c.c poset such that holds in then there is a ``natural'' c.c.c poset as well such that holds in for each .
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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