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arXiv · 0903.0810

Hausdorff gaps reconstructed from Luzin gaps

Piotr Kalemba·Szymon Plewik
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Abstract

We consider a question: Can a given AD-family be ADR for two orthogonal uncountable towers? If $b > ω_1$, then we rebuilt any AD-family of the cardinality $ω_1$ onto a Hausdorff pre-gap. Moreover, if a such AD-family is a Luzin gap, then we obtain a Hausdorff gap. Under $b = ω_1$, a similar rebuilding is impossible.

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Piotr Kalemba, Szymon Plewik. 2009-03-04. Hausdorff gaps reconstructed from Luzin gaps. https://arxiv.org/abs/0903.0810

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