{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,16]],"date-time":"2023-10-16T07:05:21Z","timestamp":1697439921305},"reference-count":6,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":11059,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1983,12]]},"abstract":"<jats:p>Indecomposability of ultrafilters was introduced by Keisler as a natural weakening of the concept of measurability. The property was first studied in depth by Chudnovsky and Chudnovsky, Prikry, and Silver (see [4] and [5]). One intriguing result of this early work was the following theorem: if <jats:italic>\u03ba<\/jats:italic> is an inaccessible cardinal and there is an indecomposable ultrafilter over <jats:italic>\u03ba<\/jats:italic>, then <jats:italic>\u03ba<\/jats:italic> is in fact \u03c9-Mahlo. Silver asked whether this result could be strengthened to say that an inaccessible cardinal carrying an indecomposable ultrafilter must be measurable. We prove in this paper that this is <jats:italic>not<\/jats:italic> the case; we construct a model where <jats:italic>\u03ba<\/jats:italic> is inaccessible and carries an indecomposable ultrafilter but <jats:italic>\u03ba<\/jats:italic> is not even weakly compact.<\/jats:p><jats:p>The results in this paper form part of the research for my doctoral dissertation at the University of California, Berkeley. I would like to thank my thesis advisor, Robert Solovay, for his patient guidance during this endeavor.<\/jats:p>","DOI":"10.2307\/2273664","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:06:05Z","timestamp":1146953165000},"page":"1000-1007","source":"Crossref","is-referenced-by-count":2,"title":["Indecomposable ultrafilters over small large cardinals"],"prefix":"10.1017","volume":"48","author":[{"given":"Michael","family":"Sheard","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200037373_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0098619"},{"key":"S0022481200037373_ref001","volume-title":"Set theory","author":"Jech","year":"1978"},{"key":"S0022481200037373_ref005","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/025\/0360276"},{"key":"S0022481200037373_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0103104"},{"key":"S0022481200037373_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0066785"},{"key":"S0022481200037373_ref003","first-page":"65","volume":"43","author":"Kunen","year":"1978","journal-title":"Saturated ideals"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200037373","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T22:11:50Z","timestamp":1558649510000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200037373\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1983,12]]},"references-count":6,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1983,12]]}},"alternative-id":["S0022481200037373"],"URL":"https:\/\/doi.org\/10.2307\/2273664","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1983,12]]}}}