Abstract
Consider the following properties of a Boolean algebra A : Pi: Every set of pairwise disjoint elements of A is countable. P2: Every chain in A is countable. For arbitrary Boolean algebras neither of these properties implies the other. The algebra of all sets of integers satisfies Pi but not P2, while the algebra of all finite or cofinite sets of real numbers satisfies P2 but not Pi. It is well known that Pi holds in any free Boolean algebra. However it is not generally realized that P2 also holds in free Boolean algebras. In fact this statement has not explicitly appeared in the literature, although it is a consequence of a theorem in topology due to N. A. Sanin [l, Theorem 50]. The following is a simple direct proof of the statement.
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