{"id":219,"date":"2011-10-11T15:27:41","date_gmt":"2011-10-11T13:27:41","guid":{"rendered":"http:\/\/logica.dmi.unisa.it\/lucaspada\/?p=219"},"modified":"2017-10-05T09:50:07","modified_gmt":"2017-10-05T08:50:07","slug":"the-dual-adjunction-between-mv-algebras-and-tychonoff-spaces","status":"publish","type":"post","link":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/219-the-dual-adjunction-between-mv-algebras-and-tychonoff-spaces\/","title":{"rendered":"The dual adjunction between MV-algebras and Tychonoff spaces"},"content":{"rendered":"<p>We offer a proof of the duality theorem for finitely presented MV-algebras and rational polyhedra, a folklore and yet fundamental result.\u00a0Our approach develops first a general dual adjunction between MV-algebras \u00a0and subspaces of \u00a0Tychonoff cubes, endowed \u00a0with the transformations that are definable in the language of MV-algebras. We then show that this dual adjunction restricts to aduality between semisimple MV-algebras and closed subspaces of \u00a0Tychonoff cubes. The duality theorem for finitely presented objects is obtained by a further specialisation. \u00a0Our treatment is aimed at showing exactly which parts of the basic theory of MV-algebras are needed in order to establish these results, with an eye towards future generalisations.<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-content\/uploads\/duality-revised.pdf\">The dual adjunction between MV-algebras and Tychonoff spaces<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We offer a proof of the duality theorem for finitely presented MV-algebras and rational polyhedra, a folklore and yet fundamental result.\u00a0Our approach develops first a general dual adjunction between MV-algebras \u00a0and subspaces of \u00a0Tychonoff cubes, endowed \u00a0with the transformations that are definable in the language of MV-algebras. We then show that this dual adjunction restricts [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[17],"tags":[30,54,35,33,55,56,28,29,38,37,32,57,39],"class_list":["post-219","post","type-post","status-publish","format-standard","hentry","category-preprint","tag-adjunction","tag-categoricalequivalence","tag-changs-completeness-theorem","tag-compact-hausdorff-spaces","tag-duality","tag-ho-lders-theorem","tag-lukasiewicz-logic","tag-mv-algebras","tag-piecewise-linear-maps","tag-rational-polyhedra","tag-tychonoff-cube","tag-w-ojcickis-theorem","tag-z-maps"],"blocksy_meta":[],"_links":{"self":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/219","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/comments?post=219"}],"version-history":[{"count":3,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/219\/revisions"}],"predecessor-version":[{"id":1158,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/219\/revisions\/1158"}],"wp:attachment":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/media?parent=219"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/categories?post=219"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/tags?post=219"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}