For an ordinal $alpha$, $sf PEA_{alpha}$ denotes the class of polyadic equality algebras of dimension $alpha$. We show that for several classes of algebras that are reducts of $PEA_{omega}$ whose signature contains all substitutions and finite cylindrifiers, if $B$ is in such a class, and $B$ is atomic, then for all $n<omega$, $Nr_nB$ is completely representable as a $PEA_n$. Conversely, we show that for any $2<n<omega$, and any variety $sf V$, between diagonal free cylindric algebras and quasipolyadic equality algebras of dimension $n$, the class of completely representable algebras in $sf V$ is not elementary.
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