{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T16:27:24Z","timestamp":1776702444226,"version":"3.51.2"},"reference-count":30,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2021,8,31]],"date-time":"2021-08-31T00:00:00Z","timestamp":1630368000000},"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":["The Review of Symbolic Logic"],"published-print":{"date-parts":[[2023,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We address Steel\u2019s Programme to identify a \u2018preferred\u2019 universe of set theory and the best axioms extending <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1755020321000447_inline1.png\"\/><jats:tex-math>\n$\\mathsf {ZFC}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> by using his multiverse axioms <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1755020321000447_inline2.png\"\/><jats:tex-math>\n$\\mathsf {MV}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> and the \u2018core hypothesis\u2019. In the first part, we examine the evidential framework for <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1755020321000447_inline3.png\"\/><jats:tex-math>\n$\\mathsf {MV}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>, in particular the use of large cardinals and of \u2018worlds\u2019 obtained through forcing to \u2018represent\u2019 alternative extensions of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1755020321000447_inline4.png\"\/><jats:tex-math>\n$\\mathsf {ZFC}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. In the second part, we address the existence and the possible features of the core of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1755020321000447_inline5.png\"\/><jats:tex-math>\n$\\mathsf {MV}_T$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula> (where <jats:italic>T<\/jats:italic> is <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1755020321000447_inline6.png\"\/><jats:tex-math>\n$\\mathsf {ZFC}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>+Large Cardinals). In the last part, we discuss the hypothesis that the core is Ultimate-<jats:italic>L<\/jats:italic>, and examine whether and how, based on this fact, the Core Universist can justify <jats:italic>V<\/jats:italic>=Ultimate-<jats:italic>L<\/jats:italic> as the best (and ultimate) extension of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1755020321000447_inline7.png\"\/><jats:tex-math>\n$\\mathsf {ZFC}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>. To this end, we take into account several strategies, and assess their prospects in the light of <jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" xlink:href=\"S1755020321000447_inline8.png\"\/><jats:tex-math>\n$\\mathsf {MV}$\n<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>\u2019s evidential framework.<\/jats:p>","DOI":"10.1017\/s1755020321000447","type":"journal-article","created":{"date-parts":[[2021,8,31]],"date-time":"2021-08-31T08:36:01Z","timestamp":1630398961000},"page":"788-812","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":5,"title":["STEEL\u2019S PROGRAMME: EVIDENTIAL FRAMEWORK, THE CORE AND ULTIMATE-<i>L<\/i>"],"prefix":"10.1017","volume":"16","author":[{"given":"JOAN","family":"BAGARIA","sequence":"first","affiliation":[]},{"given":"CLAUDIO","family":"TERNULLO","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2021,8,31]]},"reference":[{"key":"S1755020321000447_r1","doi-asserted-by":"publisher","DOI":"10.1007\/s11229-015-0819-9"},{"key":"S1755020321000447_r10","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1947.11991877"},{"key":"S1755020321000447_r3","doi-asserted-by":"publisher","DOI":"10.4007\/annals.2021.193.3.3"},{"key":"S1755020321000447_r21","doi-asserted-by":"publisher","DOI":"10.1017\/bsl.2020.5"},{"key":"S1755020321000447_r2","doi-asserted-by":"publisher","DOI":"10.2307\/2586593"},{"key":"S1755020321000447_r20","first-page":"289","volume-title":"Foundations of Mathematics. 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Available from: https:\/\/plato.stanford.edu\/entries\/large-cardinals-determinacy\/."},{"key":"S1755020321000447_r29","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511974236.023"},{"key":"S1755020321000447_r4","doi-asserted-by":"publisher","DOI":"10.1017\/bsl.2019.28"},{"key":"S1755020321000447_r30","doi-asserted-by":"publisher","DOI":"10.1017\/bsl.2016.34"},{"key":"S1755020321000447_r12","doi-asserted-by":"publisher","DOI":"10.1017\/S1755020311000359"},{"key":"S1755020321000447_r27","doi-asserted-by":"publisher","DOI":"10.1142\/S021906131750009X"},{"key":"S1755020321000447_r19","doi-asserted-by":"publisher","DOI":"10.2307\/2274569"},{"key":"S1755020321000447_r14","doi-asserted-by":"publisher","DOI":"10.2307\/421129"},{"key":"S1755020321000447_r5","first-page":"1","article-title":"More on the preservation of large cardinals by class forcing","author":"Bagaria","year":"2021","journal-title":"The Journal of Symbolic Logic"},{"key":"S1755020321000447_r9","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2014.11.004"},{"key":"S1755020321000447_r26","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-013-0357-4"},{"key":"S1755020321000447_r28","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-018-0625-4"},{"key":"S1755020321000447_r22","doi-asserted-by":"publisher","DOI":"10.1023\/A:1010600724850"},{"key":"S1755020321000447_r7","doi-asserted-by":"publisher","DOI":"10.1093\/oso\/9780198790396.001.0001"},{"key":"S1755020321000447_r18","doi-asserted-by":"publisher","DOI":"10.2307\/2586534"},{"key":"S1755020321000447_r25","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511756306.012"},{"key":"S1755020321000447_r16","unstructured":"[16] Koellner, P. 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Unpublished."},{"key":"S1755020321000447_r11","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-08-09285-X"}],"container-title":["The Review of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S1755020321000447","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,1]],"date-time":"2023-09-01T05:48:54Z","timestamp":1693547334000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S1755020321000447\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,8,31]]},"references-count":30,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2023,9]]}},"alternative-id":["S1755020321000447"],"URL":"https:\/\/doi.org\/10.1017\/s1755020321000447","relation":{},"ISSN":["1755-0203","1755-0211"],"issn-type":[{"value":"1755-0203","type":"print"},{"value":"1755-0211","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,8,31]]},"assertion":[{"value":"\u00a9 The Author(s), 2021. 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"}]}}