Abstract
The Boolean hierarchy of partitions was introduced and studied by Kosub and Wagner, primarily over the lattice of NP-sets. Here, this hierarchy is treated over lattices with the reduction property, showing that it has a much simpler structure in this instance. A complete characterization is given for the hierarchy over some important lattices, in particular, over the lattices of recursively enumerable sets and of open sets in the Baire space.
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Selivanov, V.L. Boolean Hierarchies of Partitions over a Reducible Base. Algebra and Logic 43, 44–61 (2004). https://doi.org/10.1023/B:ALLO.0000015130.31054.b3
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DOI: https://doi.org/10.1023/B:ALLO.0000015130.31054.b3