{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,15]],"date-time":"2023-11-15T00:06:37Z","timestamp":1700006797676},"reference-count":9,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2008,7,10]],"date-time":"2008-07-10T00:00:00Z","timestamp":1215648000000},"content-version":"vor","delay-in-days":9,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2008,7]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We show that the untyped <jats:italic>\u03bb<\/jats:italic> \u2010calculus can be extended with Frege's interpretation of propositional notions, provided we restrict <jats:italic>\u03b2<\/jats:italic> \u2010conversion to positive expressions. The system of illative <jats:italic>\u03bb<\/jats:italic> \u2010calculus so obtained admits a natural Scott\u2010style semantics. (\u00a9 2008 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200710053","type":"journal-article","created":{"date-parts":[[2008,7,10]],"date-time":"2008-07-10T09:52:46Z","timestamp":1215683566000},"page":"410-434","source":"Crossref","is-referenced-by-count":2,"title":["Positive Frege and its Scott\u2010style semantics"],"prefix":"10.1002","volume":"54","author":[{"given":"Thierry","family":"Libert","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2008,7,10]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","unstructured":"P.Aczel On the notion of proposition truth and set. In: The Kleene Symposium (J. Barwise H. J. Keisler and K. Kunen eds.) pp. 31\u201359 (North\u2010Holland 1980).","DOI":"10.1016\/S0049-237X(08)71252-7"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(87)90040-6"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(87)90008-X"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(89)90026-2"},{"key":"e_1_2_1_6_2","doi-asserted-by":"crossref","unstructured":"G.Gierz K. H.Hofmann K.Keimel J. D.Lawson M. W.Mislove andD. S.Scott Continuous Lattices and Domains. Encyclopedia of Mathematics and Its Applications 93 (Cambridge University Press 2003).","DOI":"10.1017\/CBO9780511542725"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1058448441"},{"key":"e_1_2_1_8_2","unstructured":"T.Libert Positive abstraction and extensionality revisited. To appear in Logique et Analyse."},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093636853"},{"key":"e_1_2_1_10_2","doi-asserted-by":"crossref","unstructured":"D.Scott Combinators and classes. In:\u03bb\u2010Calculus and Computer Science (C. B\u00f6hm ed.). Lectures Notes in Computer Science 37 pp. 1\u201326 (Springer 1975).","DOI":"10.1007\/BFb0029517"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200710053","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200710053","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,14]],"date-time":"2023-11-14T13:50:20Z","timestamp":1699969820000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200710053"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,7]]},"references-count":9,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2008,7]]}},"alternative-id":["10.1002\/malq.200710053"],"URL":"https:\/\/doi.org\/10.1002\/malq.200710053","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,7]]}}}