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Perfect effect algebras are categorically equivalent with abelian interpolation po-groups. (English) Zbl 1117.06009
The author introduces “perfect effect algebras” and shows that the category of perfect effect algebras is equivalent to the category of partially ordered abelian groups whose order is directed and has the Riesz decomposition property. It is also shown that every perfect effect algebra is a subdirect product of antilattice effect algebras with the Riesz decomposition property.

MSC:
06D35 MV-algebras
06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
03G12 Quantum logic
03B50 Many-valued logic
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