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BOOLEAN ALGEBRAS WITH NO RIGID OR HOMOGENEOUS FACTORS

By Petr Stëpânek

Abstract

A simple construction of Boolean algebras with no rigid or homogeneous factors is described. It is shown that for every uncountable cardinal k there are 2" isomorphism types of Boolean algebras of power k 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 K-distributive complete Boolean algebra can be completely embedded in a K-distributive complete Boolean algebra with no rigid or homogeneous factors

Year: 1982
OAI identifier: oai:CiteSeerX.psu:10.1.1.353.4960
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