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 sigma-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 Omega such that partial derivative(e)Omega is an F-space. (C) 2011 Elsevier B.V. All rights reserved.
loomis-sikorski theorem stone duality effect algebra state state-operator riesz decomposition property unital po-group simplex bauer simplex choquet simplex