{"id":423,"date":"2013-12-04T16:45:57","date_gmt":"2013-12-04T14:45:57","guid":{"rendered":"http:\/\/logica.dmi.unisa.it\/lucaspada\/?p=423"},"modified":"2017-10-05T09:45:35","modified_gmt":"2017-10-05T08:45:35","slug":"geometrical-dualities-for-lukasiewicz-logic","status":"publish","type":"post","link":"https:\/\/logica.dipmat.unisa.it\/lucaspada\/423-geometrical-dualities-for-lukasiewicz-logic\/","title":{"rendered":"Geometrical dualities for \u0141ukasiewicz logic"},"content":{"rendered":"<p>This is the transcript of a <em>featured talk<\/em> given on the 15th of September 2011 at the <a href=\"http:\/\/umi2011.dm.unibo.it\">XIX Congeresso dell&#8217;Unione Matematica Italiana<\/a> held in Bologna, Italy. \u00a0It is based on a joint work with <a href=\"http:\/\/marra.di.unimi.it\">Vincenzo Marra<\/a> of the University of Milan that was published in\u00a0Vincenzo Marra and Luca Spada.\u00a0<a href=\"https:\/\/logica.dipmat.unisa.it\/lucaspada\/219-the-dual-adjunction-between-mv-algebras-and-tychonoff-spaces\/\"><strong>The dual adjunction between MV-algebras and Tychonoff spaces<\/strong><\/a>,\u00a0<em>Studia Logica\u00a0<\/em><strong>100<\/strong>(1-2):253-278, 2012. S<em>pecial issue of Studia Logica in memoriam Leo Esakia (L. Beklemishev, G. Bezhanishvili, D. Mundici and Y. Venema Editors). \u00a0<\/em><\/p>\n<p>The article develops a general dual adjunction between MV-algebras (the algebraic equivalents of \u0141ukasiewicz logic) and subspaces of Tychonoff cubes, endowed with the transformations that are definable in the language of MV-algebras. Such a dual adjunction restricts to a duality between semisimple MV-algebras and closed subspaces of Tychonoff cubes. Further the duality theorem for finitely presented objects is obtained from the general adjunction by a further specialisation. The treatment is aimed at emphasising the generality of the framework considered here in the prototypical case of MV-algebras.<\/p>\n<p style=\"text-align: center;\"><a href=\"https:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-content\/uploads\/duality-UMI-revised.pdf\">Geometrical dualities for \u0141ukasiewicz logic<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>This is the transcript of a featured talk given on the 15th of September 2011 at the XIX Congeresso dell&#8217;Unione Matematica Italiana held in Bologna, Italy. \u00a0It is based on a joint work with Vincenzo Marra of the University of Milan that was published in\u00a0Vincenzo Marra and Luca Spada.\u00a0The dual adjunction between MV-algebras and Tychonoff [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2,17],"tags":[30,31,35,33,34,28,29,38,37,32,36,39],"class_list":["post-423","post","type-post","status-publish","format-standard","hentry","category-news","category-preprint","tag-adjunction","tag-categorical-duality","tag-changs-completeness-theorem","tag-compact-hausdorff-spaces","tag-holders-theorem","tag-lukasiewicz-logic","tag-mv-algebras","tag-piecewise-linear-maps","tag-rational-polyhedra","tag-tychonoff-cube","tag-wojcickis-theorem","tag-z-maps"],"blocksy_meta":[],"_links":{"self":[{"href":"https:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/423","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/comments?post=423"}],"version-history":[{"count":3,"href":"https:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/423\/revisions"}],"predecessor-version":[{"id":1150,"href":"https:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/423\/revisions\/1150"}],"wp:attachment":[{"href":"https:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/media?parent=423"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/categories?post=423"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/tags?post=423"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}