From mboxrd@z Thu Jan 1 00:00:00 1970 X-Received: by 10.107.135.195 with SMTP id r64mr4238293ioi.19.1466087579010; Thu, 16 Jun 2016 07:32:59 -0700 (PDT) X-BeenThere: homotopytypetheory@googlegroups.com Received: by 10.157.14.29 with SMTP id c29ls526565otc.10.gmail; Thu, 16 Jun 2016 07:32:58 -0700 (PDT) X-Received: by 10.157.41.201 with SMTP id g9mr30936otd.7.1466087578578; Thu, 16 Jun 2016 07:32:58 -0700 (PDT) Return-Path: Received: from mail-qk0-x233.google.com (mail-qk0-x233.google.com. [2607:f8b0:400d:c09::233]) by gmr-mx.google.com with ESMTPS id h76si688329ywc.7.2016.06.16.07.32.58 for (version=TLS1_2 cipher=ECDHE-RSA-AES128-GCM-SHA256 bits=128/128); Thu, 16 Jun 2016 07:32:58 -0700 (PDT) Received-SPF: pass (google.com: domain of marc....@gmail.com designates 2607:f8b0:400d:c09::233 as permitted sender) client-ip=2607:f8b0:400d:c09::233; Authentication-Results: gmr-mx.google.com; dkim=pass head...@gmail.com; spf=pass (google.com: domain of marc....@gmail.com designates 2607:f8b0:400d:c09::233 as permitted sender) smtp.mailfrom=marc....@gmail.com; dmarc=pass (p=NONE dis=NONE) header.from=gmail.com Received: by mail-qk0-x233.google.com with SMTP id c73so54411110qkg.2 for ; Thu, 16 Jun 2016 07:32:58 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20120113; h=mime-version:in-reply-to:references:from:date:message-id:subject:to :cc; bh=522W1753xU3M6dkfGb7Iwmkwftn3qiHcKXCOsjDP7Oo=; b=XxsLOEUYd9dtRJoDJWF4R7PenrXhfrbFjdwbEtsTqx5WFUOA9RlaffhNu812FhGqR7 akRNArk1LNCFEW4uP0y8KHFmzxUXirkHWuecaEI4a6tpBswH1+klNDCkgvI06RrvWf0A apgk/2aClpzhERfXxIatV3gfPkrI7/aJLOLowT6kNTXm6kubp1hE2oxDZno2ZWkBxPYW IxGtVTC2P0C9L10sWn8YfyhYrHGO69ZKMbEP4q0nYAYbHjrW2+5XG1zA/dxcMFICCxPA 3roPqxPDSMTEAen1AoO8iBx9tF4CQSLlI2qbNKWlLm2gAZeWmi1pnHHlwyedGtjvsn/W WFZw== X-Gm-Message-State: ALyK8tKYJd0a40TE3gBY1w209xqR8MzpV6JRBqofBCNxFf+4QRUtoK7Gn/0bQlk9N0ROLqcN61NRnw8+KtiYSw== X-Received: by 10.200.39.142 with SMTP id w14mr5236338qtw.59.1466087578408; Thu, 16 Jun 2016 07:32:58 -0700 (PDT) MIME-Version: 1.0 Received: by 10.237.38.71 with HTTP; Thu, 16 Jun 2016 07:32:57 -0700 (PDT) In-Reply-To: References: <8C57894C7413F04A98DDF5629FEC90B138B93747@Pli.gst.uqam.ca> <2850536B-0DB8-4F6D-AB3F-D5C28F6855B4@cmu.edu> From: Marc Bezem Date: Thu, 16 Jun 2016 16:32:57 +0200 Message-ID: Subject: Re: [HoTT] Is synthetic the right word? To: =?UTF-8?Q?andr=C3=A9_hirschowitz?= Cc: Andrej Bauer , Homotopy Type Theory Content-Type: multipart/alternative; boundary=001a11c13dcc5243590535661d0e --001a11c13dcc5243590535661d0e Content-Type: text/plain; charset=UTF-8 "And instead of stressing that these HoTT proofs are *also* about the usual spheres, we should rather stress that these HoTT proofs are *not at all only* about the usual spheres." What are "usual spheres" given that any classical theory of real numbers also has non-standard models? Marc --001a11c13dcc5243590535661d0e Content-Type: text/html; charset=UTF-8
"And instead of stressing that these HoTT proofs are *also* about the usual spheres, we should rather stress that these HoTT proofs are *not at all only* about the usual spheres."

What are "usual spheres" given that any classical theory of real numbers also has non-standard models?

Marc


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