{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,9]],"date-time":"2026-03-09T22:58:35Z","timestamp":1773097115308,"version":"3.50.1"},"reference-count":0,"publisher":"Cambridge University Press (CUP)","issue":"6","license":[{"start":{"date-parts":[[2003,1,17]],"date-time":"2003-01-17T00:00:00Z","timestamp":1042761600000},"content-version":"unspecified","delay-in-days":47,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Struct. Comp. Sci."],"published-print":{"date-parts":[[2002,12]]},"abstract":"<jats:p>We show that Friedman's proof of the existence of non-trivial \u03b2\u03b7-complete models \nof \u03bb<jats:sub>\u2192<\/jats:sub> can be extended to system <jats:italic>F<\/jats:italic>. We isolate a set of conditions that are sufficient to ensure \n\u03b2\u03b7-completeness for a model of <jats:italic>F<\/jats:italic> (and \u03b1-completeness at the level of types), and we discuss \nwhich class of models we get. In particular, the model introduced in Barbanera and \nBerardi (1997), having as polymorphic maps exactly all possible Scott continuous maps, is \n\u03b2\u03b7-complete, and is hence the first known complete non-syntactic model of <jats:italic>F<\/jats:italic>. In order to \nhave a suitable framework in which to express the conditions and develop the proof, we also \nintroduce the very natural notion of \u2018polymax models\u2019 of System <jats:italic>F<\/jats:italic>.<\/jats:p>","DOI":"10.1017\/s0960129502003778","type":"journal-article","created":{"date-parts":[[2003,2,7]],"date-time":"2003-02-07T14:15:20Z","timestamp":1044627320000},"page":"823-874","source":"Crossref","is-referenced-by-count":6,"title":["\u03b2\u03b7-complete models for System <i>F<\/i>"],"prefix":"10.1017","volume":"12","author":[{"given":"STEFANO","family":"BERARDI","sequence":"first","affiliation":[]},{"given":"CHANTAL","family":"BERLINE","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2003,1,17]]},"container-title":["Mathematical Structures in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0960129502003778","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T00:09:12Z","timestamp":1557187752000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0960129502003778\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,12]]},"references-count":0,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2002,12]]}},"alternative-id":["S0960129502003778"],"URL":"https:\/\/doi.org\/10.1017\/s0960129502003778","relation":{},"ISSN":["0960-1295","1469-8072"],"issn-type":[{"value":"0960-1295","type":"print"},{"value":"1469-8072","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,12]]}}}