2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/222283We 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.7 pagesLogicCombinatorics03E35text