{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,14]],"date-time":"2024-02-14T00:57:43Z","timestamp":1707872263004},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2023,1,5]],"date-time":"2023-01-05T00:00:00Z","timestamp":1672876800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2023,12]]},"abstract":"Abstract<\/jats:title>We investigate iterating the construction of \n$C^{*}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, the L<\/jats:italic>-like inner model constructed using first order logic augmented with the \u201ccofinality \n$\\omega $\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>\u201d quantifier. We first show that \n$\\left (C^{*}\\right )^{C^{*}}=C^{*}\\ne L$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> is equiconsistent with \n$\\mathrm {ZFC}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, as well as having finite strictly decreasing sequences of iterated \n$C^{*}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>s. We then show that in models of the form \n$L[U]$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> we get infinite decreasing sequences of length \n$\\omega $\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, and that an inner model with a measurable cardinal is required for that.<\/jats:p>","DOI":"10.1017\/jsl.2022.93","type":"journal-article","created":{"date-parts":[[2023,1,5]],"date-time":"2023-01-05T05:49:25Z","timestamp":1672897765000},"page":"1682-1691","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["ITERATING THE COFINALITY- CONSTRUCTIBLE MODEL"],"prefix":"10.1017","volume":"88","author":[{"ORCID":"http:\/\/orcid.org\/0000-0003-3078-059X","authenticated-orcid":false,"given":"UR","family":"YA\u2019AR","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2023,1,5]]},"reference":[{"key":"S0022481222000937_r9","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/013.1\/0281603"},{"key":"S0022481222000937_r14","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(83)90008-8"},{"key":"S0022481222000937_r2","first-page":"77","article-title":"Iterated ultrapower and Prikry\u2019s forcing","volume":"18","author":"Bukovsk\u00fd","year":"1977","journal-title":"Commentationes Mathematicae Universitatis Carolinae"},{"key":"S0022481222000937_r7","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(71)90005-2"},{"key":"S0022481222000937_r6","doi-asserted-by":"publisher","DOI":"10.1017\/S1446788700028755"},{"key":"S0022481222000937_r10","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1975-0376334-6"},{"key":"S0022481222000937_r11","unstructured":"[11] Welch, P. D. , ${C}^{\\ast }$ in $L\\left[E\\right]$ -models below ${O}^k$ . Personal communication, 2022."},{"key":"S0022481222000937_r13","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(81)90003-6"},{"key":"S0022481222000937_r1","first-page":"689","article-title":"Changing cofinality of a measurable cardinal (an alternative proof)","volume":"14","author":"Bukovsk\u00fd","year":"1973","journal-title":"Commentationes Mathematicae Universitatis Carolinae"},{"key":"S0022481222000937_r12","unstructured":"[12] Ya\u2019ar, U. , Models for short sequences of measures in the cofinality- $\\omega$ constructible model, preprint, 2021, arxiv:2109.04523."},{"key":"S0022481222000937_r4","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(75)90011-X"},{"key":"S0022481222000937_r5","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061321500124"},{"key":"S0022481222000937_r8","doi-asserted-by":"publisher","DOI":"10.4064\/fm-82-1-85-93"},{"key":"S0022481222000937_r3","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(78)90018-9"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481222000937","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,13]],"date-time":"2024-02-13T05:32:46Z","timestamp":1707802366000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481222000937\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,1,5]]},"references-count":14,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2023,12]]}},"alternative-id":["S0022481222000937"],"URL":"https:\/\/doi.org\/10.1017\/jsl.2022.93","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,1,5]]},"assertion":[{"value":"\u00a9 The Author(s), 2023. Published by Cambridge University Press on behalf of The Association for Symbolic Logic","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}