From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/2132 Path: news.gmane.org!not-for-mail From: Toby Bartels Newsgroups: gmane.science.mathematics.categories Subject: Re: What does it take to identify the field and the continuum of reals? Date: Sun, 26 Jan 2003 15:25:37 -0800 Message-ID: <20030126232537.GB9502@math-lw-n06.ucr.edu> References: <200301252120.NAA26529@coraki.Stanford.EDU> NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=us-ascii X-Trace: ger.gmane.org 1241018433 2637 80.91.229.2 (29 Apr 2009 15:20:33 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 15:20:33 +0000 (UTC) To: categories@mta.ca Original-X-From: rrosebru@mta.ca Mon Jan 27 12:33:44 2003 -0400 Return-path: Envelope-to: categories-list@mta.ca Delivery-date: Mon, 27 Jan 2003 12:33:44 -0400 Original-Received: from Majordom by mailserv.mta.ca with local (Exim 4.10) id 18dC5t-0000ZI-00 for categories-list@mta.ca; Mon, 27 Jan 2003 12:26:45 -0400 Content-Disposition: inline In-Reply-To: <200301252120.NAA26529@coraki.Stanford.EDU> User-Agent: Mutt/1.4i Original-Sender: cat-dist@mta.ca Precedence: bulk X-Keywords: X-UID: 57 Original-Lines: 20 Xref: news.gmane.org gmane.science.mathematics.categories:2132 Archived-At: Vaughan Pratt wrote in part: [about Conway's surreal numbers] >Now I conjecture that stopping just before day \epsilon_0, for the sake of >getting a set, produces a field closed under all functions whose n-th bit is >computable in time f(n) where f is definable in Peano arithmetic. And it >may well be that Conway already has a field just before day \omega^\omega, >I haven't checked but surely someone has by now (I'm very bad at keeping >up with these things, sorry). It's my understanding that you don't get a field until (just before) day K for K an inaccessible cardinal number. I'm not 100% certain about this, however! -- Toby Bartels