{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,13]],"date-time":"2025-05-13T15:35:08Z","timestamp":1747150508757,"version":"3.40.5"},"reference-count":19,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2019,12,17]],"date-time":"2019-12-17T00:00:00Z","timestamp":1576540800000},"content-version":"vor","delay-in-days":16,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2019,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We present a class forcing notion , uniformly definable for ordinals \u03b7, which forces the ground model to be the \u03b7th inner mantle of the extension, in which the sequence of inner mantles has length at least \u03b7. This answers a conjecture of Fuchs, Hamkins, and Reitz\u00a0[1] in the positive. We also show that  forces the ground model to be the \u03b7th iterated  of the extension, where the sequence of iterated s has length at least \u03b7. We conclude by showing that the lengths of the sequences of inner mantles and of iterated s can be separated to be any two ordinals you\u00a0please.<\/jats:p>","DOI":"10.1002\/malq.201800071","type":"journal-article","created":{"date-parts":[[2019,12,17]],"date-time":"2019-12-17T09:48:30Z","timestamp":1576576110000},"page":"498-510","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Inner mantles and iterated HOD"],"prefix":"10.1002","volume":"65","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7297-5654","authenticated-orcid":false,"given":"Jonas","family":"Reitz","sequence":"first","affiliation":[{"name":"Department of Mathematics New York City College of Technology City University of New York 300 Jay Street Brooklyn NY 11201 United States of America"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kameryn J.","family":"Williams","sequence":"additional","affiliation":[{"name":"Department of Mathematics University of Hawai\u2018i at M\u0101noa 2565 McCarthy Mall, Keller 401A Honolulu HI 96822 United States of America"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2019,12,17]]},"reference":[{"key":"e_1_2_6_2_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2014.11.004"},{"key":"e_1_2_6_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2011.12.006"},{"key":"e_1_2_6_4_1","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/690\/13865"},{"key":"e_1_2_6_5_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1991-0946221-X"},{"key":"e_1_2_6_6_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-08-09285-X"},{"key":"e_1_2_6_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2018.04.002"},{"key":"e_1_2_6_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(75)90011-X"},{"volume-title":"Set Theory","year":"2003","author":"Jech T. 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H.Woodin Recent developments on Cantor's Continuum Hypothesis presentation given at \u201cThe Continuum in Philosophy and Mathematics\u201d The Carlsberg Academy Copenhagen 25\u201327 November2004."},{"key":"e_1_2_6_19_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511910616.003"},{"key":"e_1_2_6_20_1","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(83)90008-8"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201800071","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201800071","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/malq.201800071","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201800071","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,7]],"date-time":"2023-09-07T22:12:20Z","timestamp":1694124740000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.201800071"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,12]]},"references-count":19,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["10.1002\/malq.201800071"],"URL":"https:\/\/doi.org\/10.1002\/malq.201800071","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"type":"print","value":"0942-5616"},{"type":"electronic","value":"1521-3870"}],"subject":[],"published":{"date-parts":[[2019,12]]},"assertion":[{"value":"2018-10-21","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-10-15","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2019-12-17","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}