Boolean algebras with no rigid or homogeneous factors

Author:
Petr Štěpánek

Journal:
Trans. Amer. Math. Soc. **270** (1982), 131-147

MSC:
Primary 06E05; Secondary 03E40

DOI:
https://doi.org/10.1090/S0002-9947-1982-0642333-3

MathSciNet review:
642333

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Abstract: A simple construction of Boolean algebras with no rigid or homogeneous factors is described. It is shown that for every uncountable cardinal there are isomorphism types of Boolean algebras of power with no rigid or homogeneous factors. A similar result is obtained for complete Boolean algebras for certain regular cardinals. It is shown that every Boolean algebra can be completely embedded in a complete Boolean algebra with no rigid or homogeneous factors in such a way that the automorphism group of the smaller algebra is a subgroup of the automorphism group of the larger algebra. It turns out that the cardinalities of antichains in both algebras are the same. It is also shown that every -distributive complete Boolean algebra can be completely embedded in a -distributive complete Boolean algebra with no rigid or homogeneous factors.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1982-0642333-3

Keywords:
Boolean algebras with no rigid or homogeneous factors,
automorphisms,
embeddings and isomorphism types of BA's,
chain conditions,
distributivity

Article copyright:
© Copyright 1982
American Mathematical Society