Representation of Perfect and Local MV-algebras

Brunella Gerla; Ciro Russo; Luca Spada

doi:10.2478/s12175-011-0015-4

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arXiv · 1002.0980

Representation of Perfect and Local MV-algebras

Brunella Gerla·Ciro Russo·Luca Spada

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Abstract

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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BibTeX RIS

Brunella Gerla, Ciro Russo, Luca Spada. 2010-02-04. Representation of Perfect and Local MV-algebras. https://doi.org/10.2478/s12175-011-0015-4

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