Loomis-Sikorski theorem and Stone duality for effect algebras with internal state

Recently Flaminio and Montagna 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 @s-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 @W such that @?"[email protected] is an F-space.

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