{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,1]],"date-time":"2026-07-01T21:28:20Z","timestamp":1782941300805,"version":"3.54.5"},"reference-count":5,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":4302,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2002,6]]},"abstract":"<jats:p>In this paper we shall repair some errors and fill some gaps in the inner model theory of [2]. The problems we shall address affect some quite basic definitions and proofs.<\/jats:p><jats:p>We shall be concerned with <jats:italic>condensation properties<\/jats:italic> of canonical inner models constructed from coherent sequences <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200009701_inline1\"\/> of extenders as in [2]. Condensation results have the general form: if <jats:italic>x<\/jats:italic> is definable in a certain way over a level <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200009701_inline2\"\/>, then either <jats:italic>x<\/jats:italic> \u2208 <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200009701_inline3\"\/>, or else from <jats:italic>x<\/jats:italic> we can reconstruct <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200009701_inline2\"\/> in a simple way.<\/jats:p><jats:p>The first condensation property considered in [2] is the <jats:italic>initial segment condition<\/jats:italic>, or ISC. In section 1 we show that the version of this condition described in [2] is too strong, in that no coherent <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200009701_inline1\"\/> in which the extenders are indexed in the manner of [2], and which is such that <jats:italic>L<\/jats:italic>[<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200009701_inline1\"\/>] satisfies the mild large cardinal hypothesis that there is a cardinal which is strong past a measurable, can satisfy the full ISC of [2]. It follows that the coherent sequences constructed in [2] do not satisfy the ISC of [2]. We shall describe the weaker ISC which these sequences do satisfy, and indicate the small changes in the arguments of [2] this new condition requires.<\/jats:p>","DOI":"10.2178\/jsl\/1190150106","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T19:13:31Z","timestamp":1197573211000},"page":"721-736","source":"Crossref","is-referenced-by-count":22,"title":["Deconstructing inner model theory"],"prefix":"10.1017","volume":"67","author":[{"given":"Ralf-Dieter","family":"Schindler","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"John","family":"Steel","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Martin","family":"Zeman","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200009701_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-22485-4"},{"key":"S0022481200009701_ref001","unstructured":"Jensen Ronald , A new fine structure for higher core models, handwritten notes."},{"key":"S0022481200009701_ref004","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(94)00036-3"},{"key":"S0022481200009701_ref003","first-page":"1285","volume":"64","author":"Neeman","year":"1999","journal-title":"A weak Dodd-Jensen lemma"},{"key":"S0022481200009701_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-21903-4"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200009701","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T01:06:35Z","timestamp":1557191195000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200009701\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,6]]},"references-count":5,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2002,6]]}},"alternative-id":["S0022481200009701"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1190150106","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,6]]}}}