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Exhaustive zero-convergence structures on Boolean algebras. (English) Zbl 0969.06011
The authors give necessary and sufficient conditions for a Boolean algebra to admit the largest possible sequential convergence structure. For the motivation and basic definitions of convergence structures see J. Jakubík’s papers [Czech. Math. J. 38(113), 520-530 (1988; Zbl 0668.54002); Math. Bohem. 123, 411-418 (1998; Zbl 0934.06017)]. Also, it is proved that for any Boolean algebra \(B\) and any sequential convergence structure \(S\) on \(B\), the join \(S\vee OS\) in the semilattice of all convergence structures on \(B\) exists. Here \(OS\) is the classical order convergence structure on \(B\).

06E10 Chain conditions, complete algebras
03G05 Logical aspects of Boolean algebras
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