{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,12,19]],"date-time":"2023-12-19T11:24:01Z","timestamp":1702985041881},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":11607,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1982,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The following problem is studied: How large and how small can the L\u00f6wenheim and Hanf numbers of unbounded logics be in relation to the most common large cardinals? The main result is that the L\u00f6wenheim number of the logic with the H\u00e4rtig-quantifier can be consistently put in between any two of the first weakly inaccessible, the first weakly Mahlo, the first weakly compact, the first Ramsey, the first measurable and the first supercompact cardinals.<\/jats:p>","DOI":"10.2307\/2273145","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:59:42Z","timestamp":1146952782000},"page":"335-346","source":"Crossref","is-referenced-by-count":5,"title":["Abstract logic and set theory. II. Large cardinals"],"prefix":"10.1017","volume":"47","author":[{"given":"Jouko","family":"V\u00e4\u00e4n\u00e4nen","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200044273_ref012","first-page":"391","volume-title":"Logic Colloquium","author":"V\u00e4\u00e4n\u00e4nen","year":"1978"},{"key":"S0022481200044273_ref002","volume-title":"Set theory","author":"Drake","year":"1974"},{"key":"S0022481200044273_ref014","doi-asserted-by":"crossref","first-page":"294","DOI":"10.1090\/S0002-9939-1980-0565357-7","article-title":"The Hanf number of L\u03c91\u03c91","volume":"79","author":"V\u00e4\u00e4n\u00e4nen","year":"1980","journal-title":"Proceedings of the American Mathematical Society"},{"key":"S0022481200044273_ref003","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19720181306"},{"key":"S0022481200044273_ref008","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1976-0540771-8"},{"key":"S0022481200044273_ref011","article-title":"Two axioms of set theory with applications to logic","volume":"17","author":"V\u00e4\u00e4n\u00e4nen","year":"1978","journal-title":"Annales Academiae Scientiarum Fennicae. Series A I Mathematica Dissertationes"},{"key":"S0022481200044273_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/BF02771565"},{"key":"S0022481200044273_ref001","first-page":"115","volume-title":"Lecture Notes in Mathematics","volume":"499","author":"Devlin","year":"1975"},{"key":"S0022481200044273_ref004","volume-title":"Set theory","author":"Jech","year":"1978"},{"key":"S0022481200044273_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(70)90013-6"},{"key":"S0022481200044273_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(76)90024-3"},{"key":"S0022481200044273_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(71)90010-6"},{"key":"S0022481200044273_ref010","first-page":"365","volume-title":"Proceedings of Symposia in Pure Mathematics","volume":"25","author":"Solovay","year":"1974"},{"key":"S0022481200044273_ref013","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(80)90005-4"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200044273","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,5,7]],"date-time":"2023-05-07T10:07:26Z","timestamp":1683454046000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200044273\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,6]]},"references-count":14,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1982,6]]}},"alternative-id":["S0022481200044273"],"URL":"https:\/\/doi.org\/10.2307\/2273145","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,6]]}}}