From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2151 Path: news.gmane.org!not-for-mail From: "Prof. Peter Johnstone" Newsgroups: gmane.science.mathematics.categories Subject: Re: Realizibility and Partial Combinatory Algebras Date: Thu, 6 Feb 2003 10:44:33 +0000 (GMT) Message-ID: References: <20030204022954.98645.qmail@web12202.mail.yahoo.com> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241018451 2740 80.91.229.2 (29 Apr 2009 15:20:51 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:20:51 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Thu Feb 6 16:43:49 2003 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Thu, 06 Feb 2003 16:43:49 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 18gsnr-0002fM-00 for categories-list@mta.ca; Thu, 06 Feb 2003 16:39:23 -0400 In-Reply-To: <20030204022954.98645.qmail@web12202.mail.yahoo.com> X-Scanner: exiscan for exim4 (http://duncanthrax.net/exiscan/) *18gjWE-0004Or-00*kYnPgBf/7Og* Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 6 Original-Lines: 24 Xref: news.gmane.org gmane.science.mathematics.categories:2151 Archived-At: On Mon, 3 Feb 2003, Galchin Vasili wrote: > > Hello, > > I understand (to some degree) full combinatory algebra, but I don't > understand the motivation behind the definition of a partial combinatory > algebra. E.g. why do we have Sxy converges/is defined? I'd like to know the answer to this too. Why does *everyone*, in writing down the definition of a PCA, include the assumption that Sxy is always defined? As far as I can see, the only answer is "because everyone else does so"; the condition is never used in the construction of realizability toposes, or in establishing any of their properties. In every case where you need to know that a particular term Sab is defined, it's easy to find a particular c such that Sabc is provably defined. Peter Johnstone