From pycyn@aol.com Fri Jun 23 09:32:08 2000 Return-Path: Received: (qmail 14718 invoked from network); 23 Jun 2000 16:32:05 -0000 Received: from unknown (10.1.10.26) by m3.onelist.org with QMQP; 23 Jun 2000 16:32:05 -0000 Received: from unknown (HELO imo-r16) (152.163.225.70) by mta1 with SMTP; 23 Jun 2000 16:32:05 -0000 Received: from Pycyn@aol.com by imo-r16.mx.aol.com (mail_out_v27.10.) id a.34.6edbd1b (4542) for ; Fri, 23 Jun 2000 12:31:49 -0400 (EDT) Message-ID: <34.6edbd1b.2684eaf3@aol.com> Date: Fri, 23 Jun 2000 12:31:47 EDT Subject: RE:Trivalent Logics To: lojban@egroups.com MIME-Version: 1.0 Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit X-Mailer: AOL 3.0 16-bit for Windows sub 41 From: pycyn@aol.com Ooops! For functional completeness the system needs min(x,y), too and that seems harder to get. Once it is gotten, however, it alone generates all of the connectives (binary, unary, more-ary), or rather the Sheffer function, min(x,y)+1, does. I think (disclaimer) that min can be defined with f1=f2 :-1 for -1, 0 otherwise and f3 as 1for 1, 0 otherwise. But my head is not functioning well in -1,0,1 arithmetic at the moment.