Hausdorff gaps reconstructed from Luzin gaps

2009/03/04 by Piotr Kalemba, Kalemba, Piotr, Szymon Plewik +1
Mathematics · #Advanced Topology and Set Theory #Algebraic Geometry and Number Theory #Rings, Modules, and Algebras #math.CO #math.LO #msc:03E35

paper · pdf · doi:10.48550/arxiv.0903.0810

7 pages

arxiv created 2009/03/04 · arxiv updated 2009/12/01

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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