  A poset is $(\omega,C)$-representable if it can be embedded into a field of
sets in such a way that all existing joins, and all existing \emph{finite}
meets are preserved. We show that the class of $(\omega,C)$-representable
posets cannot be axiomatized in first order logic using the standard language
of posets. We generalize this result to $(\alpha,\beta)$-representable posets
for certain values of $\alpha$ and $\beta$.
