From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2247 Path: news.gmane.org!not-for-mail From: Francois Lamarche Newsgroups: gmane.science.mathematics.categories Subject: Re: Kripke semantics and Alexandrov topology Date: Thu, 24 Apr 2003 08:45:53 +0200 Message-ID: <64F23624-7620-11D7-A908-0005024BFA15@loria.fr> References: <20030422214842.89385.qmail@web12203.mail.yahoo.com> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 (Apple Message framework v551) Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: quoted-printable X-Trace: ger.gmane.org 1241018524 3231 80.91.229.2 (29 Apr 2009 15:22:04 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:22:04 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Thu Apr 24 16:22:57 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 24 Apr 2003 16:22:57 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 198mGH-0007P4-00 for categories-list@mta.ca; Thu, 24 Apr 2003 16:20:01 -0300 In-Reply-To: <20030422214842.89385.qmail@web12203.mail.yahoo.com> X-Mailer: Apple Mail (2.551) Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 16 Original-Lines: 27 Xref: news.gmane.org gmane.science.mathematics.categories:2247 Archived-At: YES, because, given a poset X, the category of sheaves over X equipped=20= with the Alexandrov topology is equivalent to the category of=20 *covariant* functors X --> Set. A very important, basic fact, which=20 is at the foundation of a lot of things in topos theory and computer=20 science. Cheers, Fran=E7ois > Hello, > > I have been re-reading the chapter on intuitionism > in Goldblatt's book, specifically the section on > Kripke semantics. Am I wrong to say that Kripke > semantics is based on the Alexandrov topology > generated by the underlying poset? > > Regards, Bill >