From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/3691 Path: news.gmane.org!not-for-mail From: Vaughan Pratt Newsgroups: gmane.science.mathematics.categories Subject: Early CT problems that are still open Date: Fri, 09 Mar 2007 14:22:47 -0800 Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1241019463 9799 80.91.229.2 (29 Apr 2009 15:37:43 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:37:43 +0000 (UTC) To: categories list Original-X-From: rrosebru@mta.ca Fri Mar 9 20:08:33 2007 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Fri, 09 Mar 2007 20:08:33 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1HPoz5-0000qF-PC for categories-list@mta.ca; Fri, 09 Mar 2007 19:58:51 -0400 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 45 Original-Lines: 37 Xref: news.gmane.org gmane.science.mathematics.categories:3691 Archived-At: What early problems in category theory remain open today? Who first posed them, and when and where? Context: In December the Journal of the AMS rejected the solution of the half-century-old lattice theory problem of whether the congruence lattices of lattices are exactly the distributive algebraic lattices. Since these two classes coincide for all algebraic lattices with up to aleph_1 compact generators [Huhn 1989], one would imagine that surely the equivalence must extend to all cardinalities. Fred Wehrung recently showed it doesn't, refined by Pavel Ruzicka to show that they diverge exactly at aleph_2. For two such naturally defined classes it's very unusual to first diverge at such a high cardinal. (For elementary classes it's impossible: if they're still together at aleph_0 they're the same.) Now JAMS doesn't ordinarily cater to either lattice theory or category theory. Yet its mission statement declares JAMS to be "devoted to ... all areas of pure and applied mathematics." The general feeling among lattice theorists is that, whatever JAMS might think of those areas it is unaccustomed to serving, rejecting the solution to so celebrated an open problem is beyond the pale given their mission statement. There is no likelihood of their being overwhelmed with such so space can't be a reason. More on this at http://clp.stanford.edu . My interest here in early open CT problems is to get a sense of how comparable CT's situation is with lattice theory's. On the one hand it might seem insane for either category theorists or lattice theorists to bother the JAMS audience if they're not interested. On the other, if it's a really neat result then why hide it under a bushel? The mathematical community at large ought to be sufficiently open-minded as to appreciate such an achievement. If a category theorist were to publish the solution to a long-standing CT problem in JAMS, it would reflect well on CT, and it would lend support to JAMS's mission statement. Vaughan