From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2435 Path: news.gmane.org!not-for-mail From: Jonas Eliasson Newsgroups: gmane.science.mathematics.categories Subject: Logic preserved in double negation subtopos? Date: Tue, 2 Sep 2003 10:16:58 +0200 (CEST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241018661 4158 80.91.229.2 (29 Apr 2009 15:24:21 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:24:21 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Tue Sep 2 14:14:21 2003 -0300 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Tue, 02 Sep 2003 14:14:21 -0300 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 19uEgN-0000Kh-00 for categories-list@mta.ca; Tue, 02 Sep 2003 14:11:07 -0300 Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 3 Original-Lines: 38 Xref: news.gmane.org gmane.science.mathematics.categories:2435 Archived-At: While writing a joint paper with Steve Awodey, we came to think about the following question: Given a Grothendieck topos Sh(C), what logic is preserved by the associated sheaf functor from Sh(C) to the double negation subtopos of Sh(C)? We know that a: Sh(C) --> DNSh(C) preserves geometric logic. Since it is double negation it also preserves 0 (falsehood), negation and implication. >>From this you can draw the conclusion that a preserves the validity of formulas built up from double negation stable predicates without universal quantifiers. Presumably this has been studied in the literature, can something stronger be said about what validities are preserved, could anyone provide a reference for a general result of this kind? Grateful for any help, Jonas Eliasson ------------------------------------------ | Jonas Eliasson | | Department of Mathematics | | Uppsala University | | Sweden | | E-mail: jonase@math.uu.se | | Homepage: http://www.math.uu.se/~jonase/ | ------------------------------------------