[Note from Moderator: With the posts just sent, this discussion should come to a close. Readers of the list, and those posting to it, should be aware that it contains about 500 addresses.] *Had* Paul posted his clever hoax on, say, sci.math (which, AFAIK, he did not) where it would be widely available to J. Random Lurker, I would share Bill Lawvere's concerns. Had he placed it permanently on his web server, with a big flashing link from his home page, advertised it by spamming 100,000 random netizens, and issued a trilingual press release, I would share those concerns to a much greater extent. However, CATEGORIES is a mailing list; probably everybody who received Paul's posting also received the two debunkings, Bill's comment, and is reading this even as, er, they read this. I don't imagine that we *have* hundreds of lurkers. (Lurkers! Please identify yourselves... I'm curious.) While Bill is undoubtedly correct that not all readers of CATEGORIES share his ability to look at Paul's joke and instantly recognize not only the fallacy but its antecedents [I offer myself as a proof of the nonemptiness of the complement], surely we all have been around the block enough times to distinguish between a full formal proof and what Paul presented? Even had it been in earnest, such an announcement would justify only the reaction "Somebody thinks he's shown ... but I don't think he has circulated a complete proof yet." I suppose that it is possible that somebody, browsing at random, *might* find it in the CATEGORIES archives, in years to come, and not read ahead to find out what the world had had to say about this discovery back in the mad, exciting days of the late C20. But anybody who could do this and not realize that there was something odd going on would probably either (a) not understand why anybody should care if ZF is consistent or not, or (b) have a vague feeling that Goedel, or Escher, or somebody, already proved that, or something, didn't he? -Robert Dawson