Abstract
Answering a question posed by Hodkinson, we show that for infinite ordinals α, every atomic polyadic algebra of dimension α (PAα) 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 PAαs, is elementary. This is in sharp contrast to the cylindric algebra case.
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