hmm, I've deleted a long reply elaborating the distinction between syntactic and semantic completeness (the terminology is a mess). Just wanted to add that your

hmm, I've deleted a long reply elaborating the distinction between syntactic and semantic completeness (the terminology is a mess). Just wanted to add that your interesting point shines here: https://math.stackexchange.com/a/117914/150078 https://math.stackexchange.com/a/117914/150078