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Remarks on partitioner algebras


Authors: Alan Dow and Ryszard Frankiewicz
Journal: Proc. Amer. Math. Soc. 113 (1991), 1067-1070
MSC: Primary 03E05
DOI: https://doi.org/10.1090/S0002-9939-1991-1062385-X
MathSciNet review: 1062385
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Abstract: Partitioner algebras are defined in [1] and are a natural tool for studying the properties of maximal almost disjoint families of subsets of $ \omega $. We answer negatively two questions which were raised in [1]. We prove that there is a model in which the class of partitioner algebras is not closed under quotients and that it is consistent that there is a Boolean algebra of cardinality $ {\aleph _1}$ which is not a partitioner algebra.


References [Enhancements On Off] (What's this?)

  • [1] James E. Baumgartner and Martin Weese, Partition algebras for almost-disjoint families, Trans. Amer. Math. Soc. 274 (1982), 619-630. MR 675070 (84g:03074)
  • [2] A. Dow and P. Nyikos, Compact Hausdorff spaces with moderately large families of convergent sequences, in preparation.
  • [3] R. Frankiewicz and P. Zbierski, On partitioner-representability of Boolean algebras, Fund. Math. 135 (1990), 25-35. MR 1074646 (92b:03055)
  • [4] S. Shelah, On cardinal invariants of the continuum, Axiomatic Set Theory, Contemp. Math., vol. 31, Amer. Math. Soc., Providence, RI, 1984, pp. 183-207. MR 763901 (86b:03064)

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DOI: https://doi.org/10.1090/S0002-9939-1991-1062385-X
Article copyright: © Copyright 1991 American Mathematical Society

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