57 research outputs found
MV-algebras, multiple bets and subjective states
AbstractIn this paper MV-algebras, the algebras of L̵ukasiewicz infinite-valued logics, are interpreted in a structure of bets, and a subjective interpretation of finitely additive measures on MV-algebras is given
Representation of Perfect and Local MV-algebras
We describe representation theorems for local and perfect MV-algebras in
terms of ultraproducts involving the unit interval [0,1]. Furthermore, we give
a representation of local Abelian lattice-ordered groups with strong unit as
quasi-constant functions on an ultraproduct of the reals. All the above
theorems are proved to have a uniform version, depending only on the
cardinality of the algebra to be embedded, as well as a definable construction
in ZFC. The paper contains both known and new results and provides a complete
overview of representation theorems for such classes
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