Deconstructible classes of modules are among the main sources of approximations in relative homological algebra. They also occur in connection with abstract elementary classes (AECs). Let P = (A,<) where A = { M \in Mod-R ; Ext^i_R(M,N) = 0 for all i > 0 and all N \in C } for a class of modules C, and < is a partial order on A such that X < Y, iff Y/X \in A. Baldwin, Eklof and Trlifaj proved that P is an AEC, iff A is deconstructible and closed under arbitrary direct limits.

Let B be an arbitrary deconstructible class of modules that admits a partial order \prec such that (B,\prec) is an AEC. It is an open problem whether B is necessarily closed under arbitrary direct limits. Assuming the Axiom of Constructibility (V = L), we show that B is always closed under countable direct limits. In ZFC, we obtain the same conclusion, but under the additional assumption of B being \aleph_1-deconstructible.