{"id":28048,"date":"2021-09-10T12:48:55","date_gmt":"2021-09-10T16:48:55","guid":{"rendered":"https:\/\/blog.carlrobitaille.org\/?p=28048"},"modified":"2021-09-10T12:48:59","modified_gmt":"2021-09-10T16:48:59","slug":"the-lattice-of-sets-of-natural-numbers-is-rich","status":"publish","type":"post","link":"https:\/\/blog.carlrobitaille.org\/?p=28048","title":{"rendered":"The lattice of sets of natural numbers is rich"},"content":{"rendered":"\n<p><a href=\"http:\/\/jdh.hamkins.org\/the-lattice-of-sets-of-natural-numbers-is-rich\/\">The lattice of sets of natural numbers is rich<\/a><\/p>\n\n\n\n<figure class=\"wp-block-embed is-type-rich is-provider-twitter wp-block-embed-twitter\"><div class=\"wp-block-embed__wrapper\">\n<blockquote class=\"twitter-tweet\" data-width=\"550\" data-dnt=\"true\"><p lang=\"en\" dir=\"ltr\">The lattice of sets of natural numbers is rich. <br>It is universal for all countable orders; it has uncountable chains isomorphic to the reals; it has uncountable antichains; yet it is highly homogeneous. <a href=\"https:\/\/t.co\/wXdJzRSNCQ\">https:\/\/t.co\/wXdJzRSNCQ<\/a><\/p>&mdash; Joel David Hamkins (@JDHamkins) <a href=\"https:\/\/twitter.com\/JDHamkins\/status\/1426300422625632256?ref_src=twsrc%5Etfw\">August 13, 2021<\/a><\/blockquote><script async src=\"https:\/\/platform.twitter.com\/widgets.js\" charset=\"utf-8\"><\/script>\n<\/div><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The lattice of sets of natural numbers is rich<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[19],"tags":[],"class_list":["post-28048","post","type-post","status-publish","format-standard","hentry","category-mathematiques"],"_links":{"self":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/28048","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=28048"}],"version-history":[{"count":1,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/28048\/revisions"}],"predecessor-version":[{"id":28049,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/28048\/revisions\/28049"}],"wp:attachment":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=28048"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=28048"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=28048"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}