  Baer's Criterion for Injectivity is a basic tool of the theory of modules and
complexes of modules. Its dual version (DBC) is known to hold for all right
perfect rings, but its validity for non-right perfect rings is a complex
problem (first formulated by Faith in 1976 \cite{F}). Recently, it has turned
out that there are two classes of non-right perfect rings: 1. those for which
DBC fails in ZFC, and 2. those for which DBC is independent of ZFC. First
examples of rings in the latter class were constructed in \cite{T4}; here, we
show that this class contains all small semiartinian von Neumann regular rings
with primitive factors artinian.
