Hausdorff gaps reconstructed from Luzin gaps

Details Hausdorff gaps reconstructed from Luzin gaps Hausdorff gaps reconstructed from Luzin gaps

2009-03-04

arxiv.org/abs/0903.0810v1

Mathematics

Logic

7 pages

Scientific paper

We consider a question: Can a given AD-family be ADR for two orthogonal
uncountable towers? If $b > \omega_1$, then we rebuilt any AD-family of the
cardinality $\omega_1$ onto a Hausdorff pre-gap. Moreover, if a such AD-family
is a Luzin gap, then we obtain a Hausdorff gap. Under $b = \omega_1$, a similar
rebuilding is impossible.

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