The two-sorted algebraic theory of states
We introduce a two-sorted algebraic theory whose models are states of MV-algebras and, to within a categorical equivalence that extends Mundici's well-known one, states of Abelian lattice-groups with (strong order) unit. We discuss free states, and their relation to the universal state of an MV-algebra. We clarify the relationship of such universal states with the theory of affine representations of lattice-groups. Main result: The universal state of any locally finite MV-algebra - in particular, of any Boolean algebra - has semisimple codomain.
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Tomáš Kroupa (add twitter)
Vincenzo Marra (edit)
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Mathematics - Logic

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01/12/20 06:02PM
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mathLOb: Tomáš Kroupa, Vincenzo Marra : The two-sorted algebraic theory of states https://t.co/fbYxwams9e https://t.co/MhKDU56L09
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