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Perfect effect algebras are categorically equivalent with Abelian interpolation po-groups

Part of: Ordered structures General logic Algebraic logic

Published online by Cambridge University Press:  09 April 2009

Anatolij Dvurečenskij
Anatolij Dvurečenskij
Affiliation:
Mathematical InstituteSlovak Academy of Sciences Štefánikova 49 SK-814 73 BratislavaSlovakia e-mail: [email protected]
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Abstract

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We introduce perfect effect algebras and we show that every perfect algebra is an interval in the lexicographical product of the group of all integers with an Abelian directed interpolation po-group. To show this we introduce prime ideals of effect algebras with the Riesz decomposition property (RDP). We show that the category of perfect effect algebras is categorically equivalent to the category of Abelian directed interpolation po-groups. Moreover, we prove that any perfect effect algebra is a subdirect product of antilattice effect algebras with the RDP.

Keywords

effect algebrathe Riesz decomposition propertyradicalperfect effect algebrainterpolation po-groupunital po-groupcategorical equivalence.

MSC classification

Secondary: 06F20: Ordered abelian groups, Riesz groups, ordered linear spaces 03G12: Quantum logic 03B50: Many-valued logic
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 82 , Issue 2 , April 2007 , pp. 183 - 207
Copyright
Copyright © Australian Mathematical Society 2007

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