{"id":2482,"date":"2022-10-18T18:44:36","date_gmt":"2022-10-18T15:44:36","guid":{"rendered":"https:\/\/mathematics.haifa.ac.il\/?p=2482"},"modified":"2022-11-06T21:16:08","modified_gmt":"2022-11-06T19:16:08","slug":"colloquium-tuesday-october-25-2022-speaker-menachem-kojman-ben-gurion-title-positive-ramsey-relations-on-uncountable-sets","status":"publish","type":"post","link":"https:\/\/mathematics.haifa.ac.il\/?p=2482","title":{"rendered":"Colloquium: Tuesday, October 25, 2022. Speaker:  Menachem Kojman (Ben-Gurion). Title: &#8220;Positive Ramsey relations on uncountable sets&#8221;."},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Ramsey&#8217;s theorem,&nbsp;<img loading=\"lazy\" decoding=\"async\" width=\"67\" height=\"17\" src=\"https:\/\/s0.wp.com\/latex.php?zoom=3&amp;bg=ffffff&amp;fg=000000&amp;s=0&amp;latex=%5Cmathbb%09N%5Crightarrow%09(%5Cmathbb%09N)%5E2\" alt=\"\\mathbb N\\rightarrow (\\mathbb N)^2\">, holds for the countable infinity and has many useful applications, but, as Sierpinski discovered, fails for the real line:&nbsp;<img loading=\"lazy\" decoding=\"async\" width=\"67\" height=\"17\" src=\"https:\/\/s0.wp.com\/latex.php?zoom=3&amp;bg=ffffff&amp;fg=000000&amp;s=0&amp;latex=%5Cmathbb%09R%5Cnrightarrow%09(%5Cmathbb%09R)%5E2\" alt=\"\\mathbb R\\nrightarrow (\\mathbb R)^2\">. Strong anti-Ramsey relations are known on many uncountable cardinals and have application in general topology.&nbsp;&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">In the talk we shall survey some anti-Ramsey relations on the real line and on other uncountable cardinals and then describe a scheme for weakening &nbsp;Ramsey&#8217;s positive relation by relativizing it to a partition of pairs.&nbsp; Via this scheme, new positive Ramsey relations are shown&nbsp; to hold consistently&nbsp; at various&nbsp; uncountable cardinals. Some of their instances related to the metric topology of&nbsp;<img loading=\"lazy\" decoding=\"async\" width=\"11\" height=\"11\" src=\"https:\/\/s0.wp.com\/latex.php?zoom=3&amp;bg=ffffff&amp;fg=000000&amp;s=0&amp;latex=%5Cmathbb%09R\" alt=\"\\mathbb R\">.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Ramsey&#8217;s theorem,&nbsp;, holds for the countable infinity and has many useful applications, but, as Sierpinski discovered, fails for the real line:&nbsp;. Strong anti-Ramsey relations are known on many uncountable cardinals and have application in general topology.&nbsp;&nbsp; In the talk we&#8230;<br \/><a class=\"read-more-button\" href=\"https:\/\/mathematics.haifa.ac.il\/?p=2482\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[7],"tags":[],"class_list":["post-2482","post","type-post","status-publish","format-standard","hentry","category-colloquium"],"_links":{"self":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2482","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=2482"}],"version-history":[{"count":1,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2482\/revisions"}],"predecessor-version":[{"id":2483,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=\/wp\/v2\/posts\/2482\/revisions\/2483"}],"wp:attachment":[{"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=2482"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=2482"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathematics.haifa.ac.il\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=2482"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}