{"id":1368,"date":"2018-01-26T17:51:47","date_gmt":"2018-01-26T16:51:47","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=1368"},"modified":"2018-04-29T18:23:17","modified_gmt":"2018-04-29T16:23:17","slug":"markowksy-or-cohn","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=1368","title":{"rendered":"Markowsky or Cohn?"},"content":{"rendered":"<p>I have already mentioned Markowsky&#8217;s Theorem (1976): every chain-complete poset is a dcpo. \u00a0This is a non-trivial theorem, and I&#8217;ve given you a proof of it based on Iwamura&#8217;s Lemma and ordinals in a <a title=\"Iwamura\u2019s Lemma, Markowsky\u2019s Theorem and ordinals\" href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=563\">previous post<\/a>.\u00a0 Maurice Pouzet recently pointed me to P. M. Cohn&#8217;s book <em>Universal algebra<\/em> (1965), where you can find the same theorem already!\u00a0 Cohn&#8217;s proof is very different and does not rely on Iwamura&#8217;s Lemma.\u00a0 Let me describe it in the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=799\">full post<\/a>.<\/p>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>I have already mentioned Markowsky&#8217;s Theorem (1976): every chain-complete poset is a dcpo. \u00a0This is a non-trivial theorem, and I&#8217;ve given you a proof of it based on Iwamura&#8217;s Lemma and ordinals in a previous post.\u00a0 Maurice Pouzet recently pointed &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=1368\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-1368","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/1368","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1368"}],"version-history":[{"count":2,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/1368\/revisions"}],"predecessor-version":[{"id":1373,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/1368\/revisions\/1373"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1368"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1368"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1368"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}