 Bergman proves in a well-known unpublished note from 1986 that any at most countable distributive (∨,0)-semilattice is isomorphic to Idc "R", for some locally matricial ring "R" (over any given field).This result is extended to semilattices of cardinality at most ℵ1 in 2000 by Wehrung, by keeping only the regularity of "R" (the ring constructed by the proof is not locally matricial).The question whether "R" could be taken locally matricial in the ℵ1 case remained open for a while, until it was disproved by Wehrung in 2004.