{"id":27112,"date":"2020-12-10T13:46:51","date_gmt":"2020-12-10T18:46:51","guid":{"rendered":"https:\/\/blog.carlrobitaille.org\/?p=27112"},"modified":"2020-12-10T13:46:54","modified_gmt":"2020-12-10T18:46:54","slug":"aleph_0-and-the-axiom-of-countable-choice","status":"publish","type":"post","link":"https:\/\/blog.carlrobitaille.org\/?p=27112","title":{"rendered":"Aleph_0 and the axiom of countable choice"},"content":{"rendered":"\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\">I went deeper into the rabbit hole and learnt that to show that aleph_0 is the smallest infinite we need the axiom of countable choice! <br><br>Now I wonder about all those models where countable choice does not hold. What are those infinites smaller than aleph_0?<\/p>&mdash; Jaime Sevilla (@Jsevillamol) <a href=\"https:\/\/twitter.com\/Jsevillamol\/status\/1334810010698866688?ref_src=twsrc%5Etfw\">December 4, 2020<\/a><\/blockquote><script async src=\"https:\/\/platform.twitter.com\/widgets.js\" charset=\"utf-8\"><\/script>\n<\/div><\/figure>\n","protected":false},"excerpt":{"rendered":"","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-27112","post","type-post","status-publish","format-standard","hentry","category-mathematiques"],"_links":{"self":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/27112","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=27112"}],"version-history":[{"count":1,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/27112\/revisions"}],"predecessor-version":[{"id":27113,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=\/wp\/v2\/posts\/27112\/revisions\/27113"}],"wp:attachment":[{"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=27112"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=27112"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.carlrobitaille.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=27112"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}