From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8191 Path: news.gmane.org!not-for-mail From: Michael Barr Newsgroups: gmane.science.mathematics.categories Subject: Re: "classical" computability theory and the category of Sets Date: Fri, 4 Jul 2014 09:20:59 -0400 (EDT) Message-ID: References: Reply-To: Michael Barr NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII; format=flowed X-Trace: ger.gmane.org 1404540903 30898 80.91.229.3 (5 Jul 2014 06:15:03 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sat, 5 Jul 2014 06:15:03 +0000 (UTC) Cc: Categories mailing list To: "Vasili I. Galchin" Original-X-From: majordomo@mlist.mta.ca Sat Jul 05 08:14:56 2014 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.186]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1X3JFQ-0004d9-1v for gsmc-categories@m.gmane.org; Sat, 05 Jul 2014 08:14:56 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:46625) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1X3JF2-0004xM-Ik; Sat, 05 Jul 2014 03:14:32 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1X3JF3-0004Zr-Id for categories-list@mlist.mta.ca; Sat, 05 Jul 2014 03:14:33 -0300 In-Reply-To: User-Agent: Alpine 2.11 (LRH 23 2013-08-11) Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8191 Archived-At: A student of mine, James R. Otto worked on this for his thesis. Unfortunately, it was famously unreadable. I don't think it was published and I have lost contact with him. It was in the early 90s. Michael On Wed, 2 Jul 2014, Vasili I. Galchin wrote: > Hello Cat Theory list, > > Please be gentle. > > In the past I studied computability theory. It seems to me that > this theory is built on the category of Sets(elementary topos), i.e. > this computability theory assumes using classical logic with LEM and > boolean subobject classifier for concepts like semi-decidability, etc. > Is there a notion of intuitionistic computability theory built on > other topoi where LEM is absent from the accompanying higher logic and > the topos' subobject classifier has a internal Heyting algebra(that is > not boolean)?? Is this what realizibility delves into(I have yet to > study realizibility concepts). > > Kind regards, > > Vasya > > -- Every gun that is made, every warship launched, every rocket fired signifies, in the final sense, a theft from those who hunger and are not fed, those who are cold and are not clothed. -Dwight D. Eisenhower [For admin and other information see: http://www.mta.ca/~cat-dist/ ]