{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,24]],"date-time":"2023-09-24T04:25:29Z","timestamp":1695529529344},"reference-count":14,"publisher":"Wiley","issue":"1-2","license":[{"start":{"date-parts":[[2018,4,14]],"date-time":"2018-04-14T00:00:00Z","timestamp":1523664000000},"content-version":"vor","delay-in-days":13,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"funder":[{"name":"VCU Presidential Research Quest Fund"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2018,4]]},"abstract":"Abstract<\/jats:title>Burke proved that the generalized nonstationary ideal, denoted by NS, is universal in the following sense: every normal ideal, and every tower of normal ideals of inaccessible height, is a canonical Rudin\u2010Keisler projection of the restriction of NS to some stationary set. We investigate how far Burke's theorem can be pushed, by analyzing the universality properties of NS with respect to the wider class of \u2010systems of filters<\/jats:italic> introduced by Audrito and Steila. First we answer a question of Audrito and Steila, by proving that \u2010systems of filters do not capture all kinds of set\u2010generic embeddings. We provide a characterization of supercompactness in terms of short extenders and canonical projections of NS, without any reference to the strength of the extenders; as a corollary, NS can consistently fail to canonically project to arbitrarily strong short extenders. We prove that \u03c9\u2010cofinal towers of normal ultrafilters, e.g., the kind used to characterize I2 and I3 embeddings, are well\u2010founded if and only if they are canonical projections of NS. Finally, we provide a characterization of \u201c is J\u00f3nsson\u201d in terms of canonical projections of NS.<\/jats:p>","DOI":"10.1002\/malq.201700023","type":"journal-article","created":{"date-parts":[[2018,4,15]],"date-time":"2018-04-15T00:27:49Z","timestamp":1523752069000},"page":"103-117","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["On the universality of the nonstationary ideal"],"prefix":"10.1002","volume":"64","author":[{"given":"Sean D.","family":"Cox","sequence":"first","affiliation":[{"name":"Department of Mathematics and Applied Mathematics Virginia Commonwealth University 1015 Floyd Ave. Richmond VA 23284 United States of America"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,4,14]]},"reference":[{"key":"e_1_2_9_2_1","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2017.27"},{"key":"e_1_2_9_3_1","doi-asserted-by":"publisher","DOI":"10.2307\/2275571"},{"key":"e_1_2_9_4_1","unstructured":"B.Claverie Ideals ideal extenders and forcing axioms Ph.D. thesis (Westf\u00e4lische Wilhelms\u2010Universit\u00e4t M\u00fcnster 2010)."},{"key":"e_1_2_9_5_1","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2013.24"},{"key":"e_1_2_9_6_1","doi-asserted-by":"publisher","DOI":"10.1112\/S0024610798006462"},{"key":"e_1_2_9_7_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-5764-9_14"},{"key":"e_1_2_9_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(94)00031-W"},{"key":"e_1_2_9_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02401842"},{"key":"e_1_2_9_10_1","volume-title":"Set Theory, The Third Millennium Edition, Revised and Expanded","author":"Jech T.","year":"2003"},{"key":"e_1_2_9_11_1","volume-title":"The Higher Infinite, Large Cardinals in Set Theory from Their Beginnings","author":"Kanamori A.","year":"2003"},{"key":"e_1_2_9_12_1","volume-title":"The Stationary Tower: Notes on a Course by W. Hugh Woodin","author":"Larson P. B.","year":"2004"},{"key":"e_1_2_9_13_1","doi-asserted-by":"crossref","first-page":"279","DOI":"10.1090\/S0002-9939-1974-0327518-9","article-title":"Combinatorial characterization of supercompact cardinals","volume":"42","author":"Magidor M.","year":"1974","journal-title":"Proc. Amer. Math. Soc."},{"key":"e_1_2_9_14_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2011.12.015"},{"key":"e_1_2_9_15_1","doi-asserted-by":"publisher","DOI":"10.1515\/9783110857818"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201700023","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201700023","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,23]],"date-time":"2023-09-23T22:18:19Z","timestamp":1695507499000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.201700023"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,4]]},"references-count":14,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2018,4]]}},"alternative-id":["10.1002\/malq.201700023"],"URL":"https:\/\/doi.org\/10.1002\/malq.201700023","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,4]]},"assertion":[{"value":"2017-04-19","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2017-09-18","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2018-04-14","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}