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A countably distributive complete Boolean algebra not uncountably representable

Author: John Gregory
Journal: Proc. Amer. Math. Soc. 42 (1974), 42-46
MSC: Primary 06A40
MathSciNet review: 0332606
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Abstract: It is proved from the Continuum Hypothesis that there exists an $ \omega $-distributive complete Boolean algebra which is not $ {\omega _1}$-representable.

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

  • [1] Carol Karp, Nonaxiomatizability results for infinitary systems, J. Symbolic Logic 32 (1967), 367–384. MR 0219401
  • [2] Roman Sikorski, Boolean algebras, Second edition. Ergebnisse der Mathematik und ihrer Grenzgebiete, NeueFolge, Band 25, Academic Press Inc., New York; Springer-Verlag, Berlin-New York, 1964. MR 0177920
  • [3] Edgar C. Smith Jr., A distributivity condition for Boolean algebras, Ann. of Math. (2) 64 (1956), 551–561. MR 0086047

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Keywords: Complete Boolean algebra, $ \omega $-distributive Boolean algebra, $ {\omega _1}$-representable Boolean algebra, Continuum Hypothesis
Article copyright: © Copyright 1974 American Mathematical Society