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.