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Splitting Families and Complete Separability

  • Heike Mildenberger (a1), Dilip Raghavan (a2) and Juris Steprans (a3)
Abstract

We answer a question from Raghavan and Steprans by showing that Then we use this to construct a completely separable maximal almost disjoint family under a, partially answering a question of Shelah.

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[1] Balcar, B., Dočkálková, J., and Simon, P., Almost disjoint families of countable sets. In: Finite and infinite sets, Vol. I, II (Eger, 1981), Colloq. Math. Soc. János Bolyai 37, North-Holland, Amsterdam, 1984, 5988.
[2] Balcar, B. and Simon, P., Disjoint refinement. In: Handbook of Boolean algebras, Vol. 2, North-Holland, Amsterdam, 1989, 333388.
[3] Erdʺos, P. and Shelah, S., Separability properties of almost-disjoint families of sets. Israel J. Math. 12 (1972), 207214. http://dx.doi.org/10.1007/BF02764666
[4] Kamburelis, A. and Węglorz, B., Splittings. Arch. Math. Logic 35 (1996), 263277. http://dx.doi.org/10.1007/s001530050044
[5] Raghavan, D. and Steprans, J., On weakly tight families. Canad. J. Math., to appear. http://dx.doi.org/10.4153/CJM-2012-017-8
[6] Shelah, S., Mad families and sane player. Preprint, 0904.0816.
[7] Simon, P., A note on almost disjoint refinement. In: 24thWinter School on Abstract Analysis (Benešova Hora, 1996), Acta Univ. Carolin. Math. Phys. 37 (1996), 8999.
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Canadian Mathematical Bulletin
  • ISSN: 0008-4395
  • EISSN: 1496-4287
  • URL: /core/journals/canadian-mathematical-bulletin
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