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Depth zero Boolean algebras. (English) Zbl 1203.03057
The author characterizes the isomorphism types of depth zero Boolean algebras via the ranges of their measures. In terms of these invariants he gives a characterization of computable depth zero Boolean algebras. It is proved that the computability of a depth zero Boolean algebra depends on the level of the range of its measure in the Feiner hierarchy.

MSC:
03D45 Theory of numerations, effectively presented structures
03C57 Computable structure theory, computable model theory
06E05 Structure theory of Boolean algebras
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