{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T21:28:46Z","timestamp":1782941326819,"version":"3.54.5"},"reference-count":16,"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":8685,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1990,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We show that the modal propositional logic <jats:italic>G<\/jats:italic>, originally introduced to describe the modality \u201cit is provable that\u201d, is also sound for various interpretations using filters on ordinal numbers, for example the end-segment filters, the club filters, or the ineffable filters. We also prove that <jats:italic>G<\/jats:italic> is complete for the interpretation using end-segment filters. In the case of club filters, we show that <jats:italic>G<\/jats:italic> is complete if Jensen's principle \u25a1<jats:sub>\u03ba<\/jats:sub> holds for all \u03ba &lt; \u2135<jats:sub>\u03c9<\/jats:sub>; on the other hand, it is consistent relative to a Mahlo cardinal that <jats:italic>G<\/jats:italic> be incomplete for the club filter interpretation.<\/jats:p>","DOI":"10.2307\/2274663","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:35:29Z","timestamp":1146954929000},"page":"761-778","source":"Crossref","is-referenced-by-count":28,"title":["Infinitary combinatorics and modal logic"],"prefix":"10.1017","volume":"55","author":[{"given":"Andreas","family":"Blass","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120002613X_ref016","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(78)90031-1"},{"key":"S002248120002613X_ref015","doi-asserted-by":"publisher","DOI":"10.1007\/BF02757006"},{"key":"S002248120002613X_ref014","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/013.1\/0290961"},{"key":"S002248120002613X_ref013","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8601-8"},{"key":"S002248120002613X_ref011","first-page":"755","volume":"47","author":"Magidor","year":"1982","journal-title":"Reflecting stationary sets"},{"key":"S002248120002613X_ref010","doi-asserted-by":"publisher","DOI":"10.4064\/cm-28-2-165-180"},{"key":"S002248120002613X_ref009","first-page":"26","volume":"54","author":"Leary","year":"1989","journal-title":"Patching ideal families and enforcing reflection"},{"key":"S002248120002613X_ref008","unstructured":"Leary C. , Extensions of ideals on large cardinals, Ph.D. thesis, University of Michigan, Ann Arbor, Michigan, 1985."},{"key":"S002248120002613X_ref007","first-page":"1","volume":"24","author":"Kripke","year":"1959","journal-title":"A completeness theorem in modal logic"},{"key":"S002248120002613X_ref006","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(72)90001-0"},{"key":"S002248120002613X_ref005","volume-title":"Set theory","author":"Jech","year":"1978"},{"key":"S002248120002613X_ref004","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1093870823"},{"key":"S002248120002613X_ref002","first-page":"109","volume-title":"Infinite and finite sets","volume":"10","author":"Baumgartner","year":"1975"},{"key":"S002248120002613X_ref001","first-page":"3","volume-title":"Baku international topological conference, abstracts of reports","author":"Abashidze","year":"1987"},{"key":"S002248120002613X_ref003","volume-title":"The unprovability of consistency","author":"Boolos","year":"1979"},{"key":"S002248120002613X_ref012","first-page":"57","volume":"39","author":"Mitchell","year":"1974","journal-title":"Sets constructible from sequences of ultrafilters"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248120002613X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,18]],"date-time":"2019-05-18T21:13:30Z","timestamp":1558214010000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120002613X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,6]]},"references-count":16,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1990,6]]}},"alternative-id":["S002248120002613X"],"URL":"https:\/\/doi.org\/10.2307\/2274663","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,6]]}}}