Countable homogeneous Boolean algebras (Q793713)

The author determines the countable homogeneous Boolean algebras, where homogeneous is taken in its model-theoretic sense [e.g. {\S} 3.2 of \textit{C. C. Chang} and \textit{H. J. Keisler}, Model theory (1973; Zbl 0276.02032)]. The determination uses the three elementary invariants of a Boolean algebra ({\S} 5.5 of Chang-Keisler), and some further ones of a related character. It allows to characterize those homogeneous Boolean algebras that are strongly constructible in the sense of \textit{Yu. L. Ershov} [Decision problems and constructivizable models (Russian) (1980; Zbl 0495.03009)]. Finally, the author shows that certain cancellation laws such as: if \(A\times A\cong B\times B\) then \(A\cong B\), hold for countable homogeneous Boolean algebras, though they fail for arbitrary countable Boolean algebras as shown by \textit{J. Ketonen} [Ann. Math. (2) 108, 41--89 (1978; Zbl 0418.06006)].