{"id":181,"date":"2011-10-11T13:07:46","date_gmt":"2011-10-11T12:07:46","guid":{"rendered":"http:\/\/logica.dmi.unisa.it\/lucaspada\/?p=181"},"modified":"2017-10-05T09:52:06","modified_gmt":"2017-10-05T08:52:06","slug":"mumv-algebras-an-approach-to-fixed-points-in-lukasiewicz-logic","status":"publish","type":"post","link":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/181-mumv-algebras-an-approach-to-fixed-points-in-lukasiewicz-logic\/","title":{"rendered":"muMV-algebras: an approach to fixed points in Lukasiewicz logic"},"content":{"rendered":"<p>We study an expansion of MV-algebras, called $\\mu$MV-algebras, in which minimum and maximum fixed points are definable. The first result is that $\\mu$MV-algebras are term-wise equivalent to divisible MV$_\\Delta$ algebras, i.e. a combination of two known MV-algebras expansion: divisible MV-algebras and MV$_\\Delta$ algebras. Using methods from the two known extensions we derive a number of results about $\\mu$MV-algebras; among others: subdirect representation, standard completeness, amalgamation property and a description of the free algebra.<\/p>\n<p style=\"text-align: center;\"><a href=\"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-content\/uploads\/Articolo.pdf\">muMV-algebras: an approach to fixed points in Lukasiewicz logic<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>We study an expansion of MV-algebras, called $\\mu$MV-algebras, in which minimum and maximum fixed points are definable. The first result is that $\\mu$MV-algebras are term-wise equivalent to divisible MV$_\\Delta$ algebras, i.e. a combination of two known MV-algebras expansion: divisible MV-algebras and MV$_\\Delta$ algebras. Using methods from the two known extensions we derive a number of [&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":[74,28,29],"class_list":["post-181","post","type-post","status-publish","format-standard","hentry","category-preprint","tag-fixed-point","tag-lukasiewicz-logic","tag-mv-algebras"],"blocksy_meta":[],"_links":{"self":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/181","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=181"}],"version-history":[{"count":5,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/181\/revisions"}],"predecessor-version":[{"id":1166,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/posts\/181\/revisions\/1166"}],"wp:attachment":[{"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/media?parent=181"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/categories?post=181"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/logica.dipmat.unisa.it\/lucaspada\/wp-json\/wp\/v2\/tags?post=181"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}