Homomorphic images of -complete Boolean algebras
Author: Sabine Koppelberg
Journal: Proc. Amer. Math. Soc. 51 (1975), 171-175
MSC: Primary 06A40; Secondary 02H05
MathSciNet review: 0376475
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Abstract: It is a well-known theorem of R. S. Pierce that, for every infinite cardinal if and only if there is a complete Boolean algebra s.t. card (see [3, Theorem 25.4]). Recently, Comfort and Hager proved  that, for every infinite -complete Boolean algebra . We extend this result to the class of homomorphic images of -complete algebras, following closely Comfort's and Hager's proof. As a corollary, an improvement of Shelah's theorem on the cardinality of ultraproducts of finite sets  is derived (Theorem 2).
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-  Saharon Shelah, On the cardinality of ultraproduct of finite sets, J. Symbolic Logic 35 (1970), 83–84. MR 0325388, https://doi.org/10.2307/2271159
-  R. Sikorski, Boolean algebras, 2nd ed., Springer-Verlag, Berlin and New York, 1964.
- W. W. Comfort and A. W. Hager, Cardinality of -complete Boolean algebras, Pacific J. Math. 40 (1972), 541-545. MR 46 #7112. MR 0307997 (46:7112)
- S. Shelah, On the cardinality of ultraproducts of finite sets, J. Symbolic Logic 35 (1970), 83-84. MR 0325388 (48:3735)
- R. Sikorski, Boolean algebras, 2nd ed., Springer-Verlag, Berlin and New York, 1964.