Abstract
Answering a question posed by Hodkinson, we show that for infinite ordinals α, every atomic polyadic algebra of dimension α (PA α ) is completely representable if and only if it is completely additive. We readily infer, noting that complete additivity of an operation in an atomic algebra is a first order definable property, that the class of completely representable PA α s, is elementary. This is in sharp contrast to the cylindric algebra case.
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Communicated by R. Quackenbush.
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Ahmed, T.S. The class of completely representable polyadic algebras of infinite dimensions is elementary. Algebra Univers. 72, 371–380 (2014). https://doi.org/10.1007/s00012-014-0307-y
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DOI: https://doi.org/10.1007/s00012-014-0307-y