__ __ __ | / \ / | / | | | | _ | | |___ \__/ \__/ | \__ A N D __ __ ___ ___ ___ . __ / / \ |\ /| | \ | | | /\ | | / \ |\ | | | | | V | |__/ | | | /__\ | | | | | \| \__ \__/ | | | |__| | / \ | | \__/ | | T H E S E M I N A R Thursday, December 31, 1992 nidnight University of Pennsylvania DDDDLL 44E-7817 Linear Logic is nonregressively productive and not self-realizable, Nonmonotonic Logic is regressively nonproductive and self satisfied. Kurt W.A.J.H.Y Riellag Auspices de Beaune ABSTRACT: The amazing results quoted in the title are proved. They have unprecedented and unpredictable consequences such as: 1. Linear logic being nonregressively productive, no matter how good a theorem you produce, a harder and better one is waiting out there. 2. Linear logic is never satisfied with itself, which means that it is an infinite source of new results. In contrast, 3. Nonmonotonic logic being regressively nonproductive, no matter how bad a result you produce, there is a worse one waiting out there. 4. This does not matter anyway, since nonmonotonic logic is self satisfied. There are other incredible consequences of these results. For example, the discontinuum hypothesis is independent of NMZF (nonmonotonic ZF), and Riemann's Hypothesis gives in. The proof techniques are the most revolutionary aspect of this work. The main new concept is that of an FBI sheaf. To define an FBI sheaf, it was necessary to define a variant of Grothendieck topologies, named undercover agents. Then, an undertopos is like a topos, except that it has a subobject declassifier. An FBI site is a category with undercover agents. FBI sheaves cannot be glued, but they can be shredded. By iterating sheaf shredding long enough, we get an FBI sheaf sufficiently small that, it splits (et oui!). This is why the French say: "Voila le topo(s)". The most amazing of all is that in fact, using Freyd undercovers and the fact that A => A is intuitionistically provable, we get that every FBI sheaf over a big site is nonregressive. This is because all undercover agents eventually split. It it then an easy matter to get our fundamental results. They explain a lot, in particular about funding. Note from the moderator: I received (hard)-mail from Kurt W.A.J.H.Y Riellag late last night. Kurt W.A.J.H.Y Riellag is an illegitimate descendant of the well known Bourbaki. He has been working on these results for many years while bottling wine in the caves at Beaune. Amazingly enough, Kurt W.A.J.H.Y Riellag has no diplommas whatsoever, but he knows his wines (and cheese). Unfortunately, I learned this morning that Kurt W.A.J.H.Y Riellag went for his annual retreat at some unknown mountain winery. This means that someone here at Penn will have to give the talk if we want to hear it. I did receive a large stack of wine bottle labels containing the entire paper scribbled on them. --Jean And by the way, MERRY CHRISTMAS, and HAPPY NEW YEAR!!!!!!! The next talk after Kurt W.A.J.H.Y Riellag will be on January 18. Speaker: Ross Street. ==============================================================================