{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:22:13Z","timestamp":1777645333405,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2009,5,1]],"date-time":"2009-05-01T00:00:00Z","timestamp":1241136000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2009,5]]},"abstract":"<jats:p>In 1978, G. Plotkin [7] conjectured that for the three-element truthvalue dcpo T, if \u03ba &gt; \u03c9 then the function space [T $^{&amp;kappa;}$ \u2192 T $^{&amp;kappa;}$ ] is not a retract of T $^{&amp;kappa;}$ . In this short paper, we constructively prove a stronger result that if \u03ba &gt; \u03c9 then the function space [T $^{&amp;kappa;}$ \u2192 T $^{&amp;kappa;}$ ] is not a retract of the Cartesian product of any family of finite posets. Thus Plotkin's Conjecture is proved to be correct.<\/jats:p>","DOI":"10.3233\/fi-2009-0076","type":"journal-article","created":{"date-parts":[[2019,12,2]],"date-time":"2019-12-02T22:40:27Z","timestamp":1575326427000},"page":"301-306","source":"Crossref","is-referenced-by-count":1,"title":["A Proof of Plotkin's Conjecture"],"prefix":"10.1177","volume":"92","author":[{"given":"Lei","family":"Yinbin","sequence":"first","affiliation":[{"name":"School of Applied Mathematics, University of Electronic\r\t\t\t Science and Technology of China, Chengdu 610054, China. lybhy@163.com"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luo","family":"Maokang","sequence":"additional","affiliation":[{"name":"Yangtze Center of Mathematics, Sichuan University,\r\t\t\t Chengdu 610064, China. makaluo@scu.edu.cn"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2009,5,1]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2009-0076","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2009-0076","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:31:58Z","timestamp":1777444318000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2009-0076"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,5]]},"references-count":0,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2009,5]]}},"alternative-id":["10.3233\/FI-2009-0076"],"URL":"https:\/\/doi.org\/10.3233\/fi-2009-0076","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,5]]}}}