From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/715 Path: news.gmane.org!not-for-mail From: Steve Awodey Newsgroups: gmane.science.mathematics.categories Subject: preprint available Date: Wed, 6 May 1998 18:15:06 -0400 (EDT) Message-ID: NNTP-Posting-Host: main.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" X-Trace: ger.gmane.org 1241017138 27026 80.91.229.2 (29 Apr 2009 14:58:58 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Wed, 29 Apr 2009 14:58:58 +0000 (UTC) Cc: Alex.Simpson@dcs.ed.ac.uk, d.cubric@pmms.cam.ac.uk To: categories@mta.ca Original-X-From: cat-dist Wed May 6 20:51:50 1998 Original-Received: (from Majordom@localhost) by mailserv.mta.ca (8.8.8/8.8.8) id UAA04461 for categories-list; Wed, 6 May 1998 20:02:34 -0300 (ADT) X-Authentication-Warning: mailserv.mta.ca: Majordom set sender to cat-dist@mta.ca using -f X-Sender: awodey@cyrus.andrew.cmu.edu Original-Sender: cat-dist@mta.ca Precedence: bulk Original-Lines: 33 Xref: news.gmane.org gmane.science.mathematics.categories:715 Archived-At: Dear Colleagues, The preprint mentioned below is available from my page on the WWW, http://www.andrew.cmu.edu/user/awodey/ Please let me know if you have difficulty obtaing or printing it, or if you would like to have a paper copy sent. Steve A. ******************************************************************************* "Topological representation of the lambda-calculus" S. Awodey Abstract: The lambda-calculus can be represented topologically by assigning certain spaces to the types and certain continuous maps to the terms. Using a recent result from topos theory, the usual calculus of lambda-conversion is shown to be deductively complete with respect to such topological semantics. It is also shown to be functionally complete, in the sense that there is always a ``minimal'' topological model, in which every continuous function is lambda-definable. These results subsume earlier ones using cartesian closed categories, as well as those employing so-called Henkin and Kripke lambda-models. *******************************************************************************