{"id":214,"date":"2011-10-11T15:24:31","date_gmt":"2011-10-11T13:24:31","guid":{"rendered":"http:\/\/logica.dmi.unisa.it\/lucaspada\/?p=214"},"modified":"2017-10-05T09:50:18","modified_gmt":"2017-10-05T08:50:18","slug":"representation-of-mv-algebras-by-regular-ultrapowers-of-01","status":"publish","type":"post","link":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/214-representation-of-mv-algebras-by-regular-ultrapowers-of-01\/","title":{"rendered":"Representation of MV-algebras by regular ultrapowers of [0,1]"},"content":{"rendered":"<p>We present a <em>uniform<\/em> version of Di Nola Theorem, this enables to embed <em>all<\/em> MV-algebras of a bounded cardinality in an algebra of functions with values in a single non-standard ultrapower of the real interval <span class=\"wp-katex-eq\" data-display=\"false\">[0,1]<\/span>. This result also implies the existence, for any cardinal <span class=\"wp-katex-eq\" data-display=\"false\">\\alpha<\/span>, of a single MV-algebra in which all infinite MV-algebras of cardinality at most $\\alpha$ embed. \u00a0Recasting the above construction with <em>iterated ultrapowers<\/em>, we show how to construct such an algebra of values in a <em>definable<\/em> way, thus providing a sort of \u00a0&#8220;canonical&#8221; set of values for the functional representation.<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-content\/uploads\/final.pdf\">Representation of MV-algebras by regular ultrapowers of [0,1]<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We present a uniform version of Di Nola Theorem, this enables to embed all MV-algebras of a bounded cardinality in an algebra of functions with values in a single non-standard ultrapower of the real interval . This result also implies the existence, for any cardinal , of a single MV-algebra in which all infinite MV-algebras [&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":[58,29,61,59,60],"class_list":["post-214","post","type-post","status-publish","format-standard","hentry","category-preprint","tag-di-nola-theorem","tag-mv-algebras","tag-non-standard","tag-representation","tag-ultrapower"],"blocksy_meta":[],"_links":{"self":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/214","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=214"}],"version-history":[{"count":5,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/214\/revisions"}],"predecessor-version":[{"id":1159,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/214\/revisions\/1159"}],"wp:attachment":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/media?parent=214"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/categories?post=214"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/tags?post=214"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}