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arXiv · 1006.0503

Loomis--Sikorski Theorem and Stone Duality for Effect Algebras with Internal State

D. Buhagiar·E. Chetcutti·A. Dvurečenskij
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Abstract

Recently Flaminio and Montagna, \cite{FlMo}, extended the language of MV-algebras by adding a unary operation, called a state-operator. This notion is introduced here also for effect algebras. Having it, we generalize the Loomis--Sikorski Theorem for monotone $σ$-complete effect algebras with internal state. In addition, we show that the category of divisible state-morphism effect algebras satisfying (RDP) and countable interpolation with an order determining system of states is dual to the category of Bauer simplices $Ω$ such that $\partial_e Ω$ is an F-space.

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D. Buhagiar, E. Chetcutti, A. Dvurečenskij. 2010-06-02. Loomis--Sikorski Theorem and Stone Duality for Effect Algebras with Internal State. https://arxiv.org/abs/1006.0503

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