A countably distributive complete Boolean algebra not uncountably representable
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- by John Gregory PDF
- Proc. Amer. Math. Soc. 42 (1974), 42-46 Request permission
Abstract:
It is proved from the Continuum Hypothesis that there exists an $\omega$-distributive complete Boolean algebra which is not ${\omega _1}$-representable.References
- Carol Karp, Nonaxiomatizability results for infinitary systems, J. Symbolic Logic 32 (1967), 367–384. MR 219401, DOI 10.2307/2270780
- Roman Sikorski, Boolean algebras, 2nd ed., Ergebnisse der Mathematik und ihrer Grenzgebiete, (N.F.), Band 25, Academic Press, Inc., New York; Springer-Verlag, Berlin-New York, 1964. MR 0177920
- Edgar C. Smith Jr., A distributivity condition for Boolean algebras, Ann. of Math. (2) 64 (1956), 551–561. MR 86047, DOI 10.2307/1969602
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 42 (1974), 42-46
- MSC: Primary 06A40
- DOI: https://doi.org/10.1090/S0002-9939-1974-0332606-7
- MathSciNet review: 0332606