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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Remarks on partitioner algebras


Authors: Alan Dow and Ryszard Frankiewicz
Journal: Proc. Amer. Math. Soc. 113 (1991), 1067-1070
MSC: Primary 03E05
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.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1991-1062385-X
PII: S 0002-9939(1991)1062385-X
Article copyright: © Copyright 1991 American Mathematical Society