{"id":3709,"date":"2024-01-07T15:36:05","date_gmt":"2024-01-07T20:36:05","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/boyland\/?page_id=3709"},"modified":"2026-03-19T08:10:23","modified_gmt":"2026-03-19T12:10:23","slug":"alejandro-poveda","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/boyland\/alejandro-poveda\/","title":{"rendered":"Alejandro Poveda"},"content":{"rendered":"\r\n<section class=\"fullwidth-text-block\">\r\n\t<div class=\"container px-0 pt-5\">\r\n\t\t<div class=\"row align-items-start\">\r\n\t\t\t<div class=\"col-12\">\r\n\t\t\t\t\n<h1 class=\"wp-block-heading\">Alejandro Poveda<\/h1>\n\n\n\n<h3 class=\"wp-block-heading\">Cardinal arithmetic and compactness phenomena in set theory<\/h3>\n\n\n\n<p>In his 1984 influential paper, G. Cantor discovered the existence of various types of infinites, setting the stage for the development of cardinal arithmetic \u2014 a core area of research in modern set theory. Another central theme in set theory is the study of compactness phenomena. Compactness is the phenomenon by which the properties of a mathematical structure (a group, a graph, a topological space, etc) are determined by the behavior of its small substructures. The primary focus of this colloquium is to examine the extent to which certain cardinal-arithmetic configurations influence the emergence of compactness phenomena. We shall begin the presentation providing a historical overview of the field of cardinal arithmetic culminating our exposition with the so-called Singular Cardinal Hypothesis (SCH). Later we will discuss compactness phenomena, putting the focus on two prominent combinatorial principles; namely, the Tree Property (TP) and Stationary Reflection (SR). Our discussion will be concluded with a presentation of a few recent results analyzing the interplay between the SCH, the TP and SR. Incidentally, those results answer two long-standing open problems by M. Magidor.<\/p>\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":146,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-3709","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/3709","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/users\/146"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/comments?post=3709"}],"version-history":[{"count":2,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/3709\/revisions"}],"predecessor-version":[{"id":3795,"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/pages\/3709\/revisions\/3795"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/boyland\/wp-json\/wp\/v2\/media?parent=3709"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}