Representation of MV-algebras by regular ultrapowers of [0,1]
We present a uniform version of Di Nola Theorem, this enables to embed all MV-algebras of a bounded cardinality in an algebra of functions with values in a single non-standard ultrapower of the real interval [0,1]. This result also implies the existence, for any cardinal \alpha, of a single MV-algebra in which all infinite MV-algebras of cardinality at most $\alpha$ embed. Recasting the above construction with iterated ultrapowers, we show how to construct such an algebra of values in a definable way, thus providing a sort of “canonical” set of values for the functional representation.
Representation of MV-algebras by regular ultrapowers of [0,1]
Tags: Di Nola Theorem, MV-algebras, non standard, Representation, Ultrapower
