Jan Trlifaj, Charles University Prague
Faith's problem on R-projectivity is undecidable

In 1976, Faith asked for a characterization of the rings R such that each R-projective module is projective, that is, the Dual Baer Criterion holds in Mod-R. Such rings were called right testing. Sandomierski proved that each right perfect ring is right testing. Puninski et al. have recently shown for a number of non-right perfect rings that they are not right testing (in ZFC), and noticed the consistency with ZFC of the statement `each right testing ring is right perfect.'