Club guessing principles imply the existence of long towers of almost disjoint sets, yielding new non-saturation results for ideals extending the nonstationary ideal.
BAUMGARTNER, Almost disjoint sets, the dense set problem and the partition calculus, Annals of Mathematical Logic 10 (1976), 401-439
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Towers and clubs
Club guessing principles imply the existence of long towers of almost disjoint sets, yielding new non-saturation results for ideals extending the nonstationary ideal.