From mboxrd@z Thu Jan 1 00:00:00 1970 X-Msuck: nntp://news.gmane.io/gmane.science.mathematics.categories/8177 Path: news.gmane.org!not-for-mail From: Robin Adams Newsgroups: gmane.science.mathematics.categories Subject: Re: Intro to higher order categorical logic question Date: Fri, 27 Jun 2014 11:37:04 +0200 Message-ID: References: Reply-To: Robin Adams NNTP-Posting-Host: plane.gmane.org Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit X-Trace: ger.gmane.org 1403988962 28592 80.91.229.3 (28 Jun 2014 20:56:02 GMT) X-Complaints-To: usenet@ger.gmane.org NNTP-Posting-Date: Sat, 28 Jun 2014 20:56:02 +0000 (UTC) To: categories@mta.ca Original-X-From: majordomo@mlist.mta.ca Sat Jun 28 22:55:57 2014 Return-path: Envelope-to: gsmc-categories@m.gmane.org Original-Received: from smtp3.mta.ca ([138.73.1.186]) by plane.gmane.org with esmtp (Exim 4.69) (envelope-from ) id 1X0zf9-0002k6-W2 for gsmc-categories@m.gmane.org; Sat, 28 Jun 2014 22:55:56 +0200 Original-Received: from mlist.mta.ca ([138.73.1.63]:45571) by smtp3.mta.ca with esmtp (Exim 4.80) (envelope-from ) id 1X0zdt-0008FF-It; Sat, 28 Jun 2014 17:54:37 -0300 Original-Received: from majordomo by mlist.mta.ca with local (Exim 4.71) (envelope-from ) id 1X0zdt-0003OT-H8 for categories-list@mlist.mta.ca; Sat, 28 Jun 2014 17:54:37 -0300 In-Reply-To: Precedence: bulk Xref: news.gmane.org gmane.science.mathematics.categories:8177 Archived-At: Dear Vasya, The equivalence is given in Propositions 2.1 and 2.2 and Theorem 2.4. We can introduce the logical connectives as primitives and then define equality; or we can introduce equality as a primitive and define the logical connectives in terms of =. Either way gives the same set of derivable judgements. -- Robin Adams On 19/06/14 09:12, Vasili I. Galchin wrote: > Hello, > > In the "Introduction to Part II" paragraph one , two type > theories are mentioned. The last sentence of this paragraph states > "These two versions are shown to be equivalent, although the > second(equality .. my words) is useful for describing the internal > language of a topos". Question: In what sense are these two type > theory equivalent? In some technical sense? > > > Kind regards, > > Vasya [For admin and other information see: http://www.mta.ca/~cat-dist/ ]