From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/612 Path: news.gmane.org!not-for-mail From: categories Newsgroups: gmane.science.mathematics.categories Subject: Re: Challenge from Harvey Friedman Date: Fri, 23 Jan 1998 19:37:43 -0400 (AST) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: TEXT/PLAIN; charset=US-ASCII X-Trace: ger.gmane.org 1241017071 26505 80.91.229.2 (29 Apr 2009 14:57:51 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:57:51 +0000 (UTC) To: categories Original-X-From: cat-dist Fri Jan 23 19:38:27 1998 Original-Received: (from cat-dist@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id TAA09366; Fri, 23 Jan 1998 19:37:44 -0400 (AST) Original-Lines: 24 Xref: news.gmane.org gmane.science.mathematics.categories:612 Archived-At: Date: Fri, 23 Jan 1998 16:32:35 -0600 (CST) From: David Yetter Dear Fellow Categorists: I am personally not likely to take up Harvey Friedman's challenge, having long been doing "category theory as algebra" rather than "category theory as foundations". I would like to point out, though that Friedman has deliberately chosen as a test case real analysis, a subject which exists only to simulate the existence of fluxions on the basis of foundations tied to two-valued logic. How about asking Friedman to give an elegant, elementary foundation for rings satisfying the Kock-Lawvere axioms? The use of an axiom schema in which arbitrarily complex formulae may be subsituted also seems a bit of a dodge. At first glance, elementary topoi plus NNO, well-pointed and choice still doesn't need such things (but I could be wrong, not having thought much about it for years). Best Thoughts, David Yetter