From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/4858 Path: news.gmane.org!not-for-mail From: Jaap van Oosten Newsgroups: gmane.science.mathematics.fom,gmane.science.mathematics.categories Subject: paper: Partial Combinatory Algebras of Functions Date: Thu, 21 May 2009 16:12:36 +0200 Message-ID: <4A156154.5030606@uu.nl> References: <8CBA196F31E8553-134C-6AC@WEBMAIL-DY09.sysops.aol.com> <4A0BE853.1080708@uu.nl> Reply-To: Foundations of Mathematics NNTP-Posting-Host: lo.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset="us-ascii" Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1242932354 6788 80.91.229.12 (21 May 2009 18:59:14 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Thu, 21 May 2009 18:59:14 +0000 (UTC) To: Foundations of Mathematics , Categories Original-X-From: fom-bounces-+I05ep9qJbk3uPMLIKxrzw@public.gmane.org Thu May 21 20:59:07 2009 Return-path: Envelope-to: gsmf-fom-Uylq5CNFT+jYtjvyW6yDsg@public.gmane.org Original-Received: from mx.cims.nyu.edu ([128.122.80.107]) by lo.gmane.org with esmtp (Exim 4.50) id 1M7DTu-0006T7-FG for gsmf-fom-Uylq5CNFT+jYtjvyW6yDsg@public.gmane.org; Thu, 21 May 2009 20:59:06 +0200 Original-Received: from mx.cims.nyu.edu (localhost [127.0.0.1]) by mx.cims.nyu.edu (8.13.8+Sun/8.13.8) with ESMTP id n4LIo3Ec028724; Thu, 21 May 2009 14:50:09 -0400 (EDT) Original-Received: from uu01msg-smtp01.soliscom.uu.nl (uu01msg-smtp01.soliscom.uu.nl [131.211.4.101]) by mx.cims.nyu.edu (8.13.8+Sun/8.13.8) with ESMTP id n4LEUHCt008732 for ; Thu, 21 May 2009 10:30:17 -0400 (EDT) Original-Received: from uu01msg-exb05.soliscom.uu.nl ([131.211.4.74]) by uu01msg-smtp01.soliscom.uu.nl with Microsoft SMTPSVC(6.0.3790.1830); Thu, 21 May 2009 16:13:11 +0200 Original-Received: from uu01msg-exf04.soliscom.uu.nl ([131.211.4.109]) by uu01msg-exb05.soliscom.uu.nl with Microsoft SMTPSVC(6.0.3790.1830); Thu, 21 May 2009 16:13:11 +0200 Original-Received: from [131.211.23.8] ([131.211.23.8]) by uu01msg-exf04.soliscom.uu.nl with Microsoft SMTPSVC(6.0.3790.1830); Thu, 21 May 2009 16:13:11 +0200 User-Agent: Thunderbird 1.5.0.10 (X11/20070304) In-Reply-To: <4A0BE853.1080708-qTWcuMntz1Q@public.gmane.org> X-OriginalArrivalTime: 21 May 2009 14:13:11.0036 (UTC) FILETIME=[45B873C0:01C9DA1E] X-Scanned-By: MIMEDefang 2.58 on 128.122.80.107 X-Scanned-By: MIMEDefang 2.58 on 128.122.80.107 X-Greylist: Sender IP whitelisted, not delayed by milter-greylist-3.0 (mx.cims.nyu.edu [127.0.0.1]); Thu, 21 May 2009 14:50:11 -0400 (EDT) X-Greylist: Delayed for 00:17:33 by milter-greylist-3.0 (mx.cims.nyu.edu [128.122.80.107]); Thu, 21 May 2009 10:30:19 -0400 (EDT) X-Mailman-Approved-At: Thu, 21 May 2009 14:48:32 -0400 X-BeenThere: fom-+I05ep9qJbk3uPMLIKxrzw@public.gmane.org X-Mailman-Version: 2.1.6 Precedence: list List-Id: Foundations of Mathematics List-Unsubscribe: , List-Archive: List-Post: List-Help: List-Subscribe: , Original-Sender: fom-bounces-+I05ep9qJbk3uPMLIKxrzw@public.gmane.org Errors-To: fom-bounces-+I05ep9qJbk3uPMLIKxrzw@public.gmane.org Xref: news.gmane.org gmane.science.mathematics.fom:5395 gmane.science.mathematics.categories:4858 Archived-At: A new paper of mine is available on the Arxiv: http://front.math.ucdavis.edu/0905.2665 *Abstract:* We employ the notions of `sequential function' and `interrogation' (dialogue) in order to define new partial combinatory algebra structures on sets of functions. These structures are analyzed using J. Longley's preorder-enriched category of partial combinatory algebras and decidable applicative structures.We also investigate total combinatory algebras of partial functions. One of the results is, that every realizability topos is a quotient of a realizability topos on a total combinatory algebra.