Abstract
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 α, of a single MV-algebra in which all infinite MV-algebras of cardinality at most α 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.
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Di Nola, A., Lenzi, G. & Spada, L. Representation of MV-algebras by regular ultrapowers of [0, 1]. Arch. Math. Logic 49, 491–500 (2010). https://doi.org/10.1007/s00153-010-0182-y
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DOI: https://doi.org/10.1007/s00153-010-0182-y