The discussion and responses on sub-structures of free structures got me thinking about a problem that bothered to me some time a go. Suppose an equational class V has the following property: (1) if A and B are FINITELY GENERATED V-agebras whose coproduct is free, then A and B are both free. Does this imply that V has the prorerty that (2) if A and B are ANY V-agebras whose coproduct is free, then A and B are both free? I proved in 1983 that the variety of vector-lattices (= abelian lattice-ordered groups with order-preserving action by positive real numbers) has (1), using PL topology. (In the variety of vector-lattices, projective does not imply free, so this result has some content.) In fact, if V = vector-lattices, the following is true: (1a) if A and B are ANY V-agebras whose coproduct is FINITELY GENERATED and free, then A and B are both free. BUT, I was never able to show that the variety of vector-lattices has (2). Does (2) follow from (1) or from (1a) by any general theorems of universal algebra, model-theory, etc.? James Madden