{"id":2179,"date":"2019-12-23T16:07:12","date_gmt":"2019-12-23T15:07:12","guid":{"rendered":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=2179"},"modified":"2023-03-20T11:37:12","modified_gmt":"2023-03-20T10:37:12","slug":"the-rasiowa-sikorski-lemma-and-the-baire-property","status":"publish","type":"post","link":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=2179","title":{"rendered":"The Rasiowa-Sikorski lemma and the Baire property"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Merry Christmas!  And a Happy New Year, too.  There are incredible links between logic and topology, and I would like to start with something called the Rasiowa-Sikorski lemma in logic.  That is a theorem that states the existence of certain prime filters in a Boolean algebra, and which was invented as a clean justification of a completeness argument for first-order logic.  Robert Goldblatt realized in a 2012 paper that the Rasiowa-Sikorski lemma is a consequence of the fact that all compact Hausdorff spaces are Baire (plus some Stone duality, which is the main bridge between logic and topology).  This is a beautiful argument&#8230; read the <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?page_id=2152\">full post<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Merry Christmas! And a Happy New Year, too. There are incredible links between logic and topology, and I would like to start with something called the Rasiowa-Sikorski lemma in logic. That is a theorem that states the existence of certain &hellip; <a href=\"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/?p=2179\">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":[62,14,65],"class_list":["post-2179","post","type-post","status-publish","format-standard","hentry","category-uncategorized","tag-baire-property","tag-filters","tag-logic"],"_links":{"self":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/2179","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=2179"}],"version-history":[{"count":1,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/2179\/revisions"}],"predecessor-version":[{"id":2180,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=\/wp\/v2\/posts\/2179\/revisions\/2180"}],"wp:attachment":[{"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2179"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2179"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/projects.lsv.ens-paris-saclay.fr\/topology\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2179"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}