Hausdorff gaps reconstructed from Luzin gaps
Abstract
We consider a question: Can a given AD-family be ADR for two orthogonal uncountable towers? If b > ω1, then we rebuilt any AD-family of the cardinality ω1 onto a Hausdorff pre-gap. Moreover, if a such AD-family is a Luzin gap, then we obtain a Hausdorff gap. Under b = ω1, a similar rebuilding is impossible.
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