Representation of Perfect and Local MV-algebras

Details Representation of Perfect and Local MV-algebras Representation of Perfect and Local MV-algebras

2010-02-04

arxiv.org/abs/1002.0980v1

Mathematica Slovaca (2011), 61(3): 327--340

Mathematics

Logic

Scientific paper

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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