{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,19]],"date-time":"2023-10-19T06:11:11Z","timestamp":1697695871100},"reference-count":14,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,7,24]],"date-time":"2006-07-24T00:00:00Z","timestamp":1153699200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2006,8]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We extend the gap 1 cardinal transfer theorem (<jats:italic>\u03ba<\/jats:italic> <jats:sup>+<\/jats:sup>, <jats:italic>\u03ba<\/jats:italic> ) \u2192 (<jats:italic>\u03bb<\/jats:italic> <jats:sup>+<\/jats:sup>, <jats:italic>\u03bb<\/jats:italic> ) to any language of cardinality \u2264<jats:italic>\u03bb<\/jats:italic>, where <jats:italic>\u03bb<\/jats:italic> is a regular cardinal. This transfer theorem has been proved by Chang under GCH for countable languages and by Silver in some cases for bigger languages (also under GCH). We assume the existence of a coarse (<jats:italic>\u03bb<\/jats:italic>, 1)\u2010morass instead of GCH. (\u00a9 2006 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200510038","type":"journal-article","created":{"date-parts":[[2006,7,24]],"date-time":"2006-07-24T14:47:02Z","timestamp":1153752422000},"page":"340-350","source":"Crossref","is-referenced-by-count":2,"title":["A gap 1 cardinal transfer theorem"],"prefix":"10.1002","volume":"52","author":[{"given":"Luis M.","family":"Villegas\u2010Silva","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,7,24]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.2307\/2035887"},{"key":"e_1_2_1_3_2","unstructured":"C. C.Chang andH. J.Keisler Model Theory 3rd ed. (North\u2010Holland 1993)."},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","unstructured":"K.Devlin Constructibility (Springer\u2010Verlag 1984).","DOI":"10.1007\/978-3-662-21723-8"},{"key":"e_1_2_1_5_2","doi-asserted-by":"crossref","unstructured":"H. D.Donder Coarse morasses inL. In: Lecture Notes in Mathematics 872 pp. 37\u201354 (Springer\u2010Verlag 1981).","DOI":"10.1007\/BFb0098618"},{"key":"e_1_2_1_6_2","doi-asserted-by":"crossref","unstructured":"R. B.Jensen andC.Karp Primitive recursive set functions. In: Axiomatic Set Theory (D. Scott ed.). Proceedings of Symposia in Pure Mathematics13 pp. 143\u2013167 (AMS 1971).","DOI":"10.1090\/pspum\/013.1\/0281602"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(72)90001-0"},{"key":"e_1_2_1_8_2","unstructured":"R. B.Jensen private communication."},{"key":"e_1_2_1_9_2","unstructured":"R. B.Jensen The (\u03ba \u03b2)\u2010morass. Unpublished manuscript."},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1190150156"},{"key":"e_1_2_1_11_2","unstructured":"P. M.Iturralde J. A. N.Valencia andL. M.Villegas\u2010Silva Weakly compact cardinals and\u03ba\u2010torsionless modules. In preparation."},{"key":"e_1_2_1_12_2","doi-asserted-by":"crossref","unstructured":"G. E.Sacks Higher Recursion Theory (Springer\u2010Verlag 1990).","DOI":"10.1007\/978-3-662-12013-2"},{"key":"e_1_2_1_13_2","doi-asserted-by":"crossref","unstructured":"L.Stanley A short course on gap\u2010one morasses with a review of the fine structure ofL. In: Surveys in Set Theory pp. 197\u2013243. London Math. Soc. Lecture Note Series 87 (Cambridge University Press 1983).","DOI":"10.1017\/CBO9780511758867.008"},{"key":"e_1_2_1_14_2","unstructured":"L. M.Villegas\u2010Silva The two cardinal transfer theorem for languages of arbitrarily cardinality. Submitted to the Journal of Symbolic Logic."},{"key":"e_1_2_1_15_2","unstructured":"H. J.Wunderlich \u00dcber zwei\u2010Kardinalzahl\u2010Probleme. Diplomarbeit Universit\u00e4t Freiburg 1981."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200510038","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200510038","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T18:05:27Z","timestamp":1697652327000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200510038"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,7,24]]},"references-count":14,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2006,8]]}},"alternative-id":["10.1002\/malq.200510038"],"URL":"https:\/\/doi.org\/10.1002\/malq.200510038","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,7,24]]}}}