From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/5997 Path: news.gmane.org!not-for-mail From: Vaughan Pratt Newsgroups: gmane.science.mathematics.categories Subject: Re: Reducibility Date: Tue, 20 Jul 2010 23:06:34 -0700 Message-ID: References: Reply-To: Vaughan Pratt NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=ISO-8859-1; format=flowed Content-Transfer-Encoding: 7bit X-Trace: dough.gmane.org 1279721413 10446 80.91.229.12 (21 Jul 2010 14:10:13 GMT) X-Complaints-To: usenet@dough.gmane.org NNTP-Posting-Date: Wed, 21 Jul 2010 14:10:13 +0000 (UTC) To: categories@mta.ca Original-X-From: categories@mta.ca Wed Jul 21 16:10:10 2010 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from mailserv.mta.ca ([138.73.1.1]) by lo.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1ObZzu-0004ky-1W for gsmc-categories@m.gmane.org; Wed, 21 Jul 2010 16:10:10 +0200 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.61) (envelope-from ) id 1ObZPC-00050f-NT for categories-list@mta.ca; Wed, 21 Jul 2010 10:32:14 -0300 In-Reply-To: Original-Sender: categories@mta.ca Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:5997 Archived-At: The question as posed makes no sense. To begin with, there are too many groups to form a set, so you need to pose this as a question about classes rather than sets, and f needs to map classes instead of sets. Second, you must first specify a larger class of which the class of all groups is a proper subclass. Otherwise what does it mean for x not to be a member of A? In this case, what does it mean not to be a group? If you make the larger class "everything" then f has an unmanageably large domain. What if you apply f to an anteater, for example? Vaughan Pratt On 7/19/2010 9:46 AM, Russ Abbott wrote: > Hi, > > I apologize if this is off topic. I'm not sure where to direct this > question. > > I'm interested in when one can say that one theory is reducible to another. > Reducibility is defined: a set A is T-reducible to a set B if there is a > function f of type T such that x is a member of A if and only if f(x) is a > member of B. Mathematical groups are defined in terms of a 0 element, other > elements, and an operation with certain properties. Let A be the set > of mathematical > groups (set of models of groups?). Is there an interesting set B and > function type T so that A is T-reducible to B? > > First of all, is that an interesting question to ask? If so, how would one > go about thinking about it? > > Thanks for any help or pointers you can give me. > > -- Russ Abbott > ______________________________________ > > Professor, Computer Science > California State University, Los Angeles > > cell: 310-621-3805 > Google voice: 424-2Blue4 > blog: http://russabbott.blogspot.com/ > vita: http://sites.google.com/site/russabbott/ > ______________________________________ > [For admin and other information see: http://www.mta.ca/~cat-dist/ ]