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Loomis--Sikorski Theorem and Stone Duality for Effect Algebras with Internal State
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 -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 such that is an F-space
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