{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,23]],"date-time":"2026-06-23T12:40:24Z","timestamp":1782218424871,"version":"3.54.5"},"reference-count":9,"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":8685,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1990,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We characterize, in terms of determinacy, the existence of 0<jats:sup>##<\/jats:sup> as well as the existence of each of the following: 0<jats:sup>###<\/jats:sup>, 0<jats:sup>####<\/jats:sup>, 0<jats:sup>#####<\/jats:sup>,\u2026. For <jats:italic>\u03ba \u0404 \u03c9<\/jats:italic>, we define two classes of sets, <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200025937_inline1\"\/> and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200025937_inline2\"\/>, which lie strictly between <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200025937_inline3\"\/> and <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200025937_inline4\"\/>. We also define 0<jats:sup>1#<\/jats:sup> as<jats:sup>#<\/jats:sup> and in general, 0<jats:sup>(<jats:italic>k<\/jats:italic>+1)#<\/jats:sup> as (0<jats:sup><jats:italic>k<\/jats:italic>#<\/jats:sup>)<jats:sup>#<\/jats:sup>. We then show that the existence of 0<jats:sup>(<jats:italic>k<\/jats:italic> + 1)#<\/jats:sup> is equivalent to the determinacy of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200025937_inline5\"\/> as well as the determinacy of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200025937_inline2\"\/>.<\/jats:p>","DOI":"10.2307\/2274643","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:35:29Z","timestamp":1146940529000},"page":"502-525","source":"Crossref","is-referenced-by-count":14,"title":["The equivalence of determinacy and iterated sharps"],"prefix":"10.1017","volume":"55","author":[{"given":"Derrick Albert","family":"Dubose","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200025937_ref008","doi-asserted-by":"crossref","first-page":"287","DOI":"10.4064\/fm-66-3-287-291","article-title":"Measurable cardinals and analytic games","volume":"66","author":"Martin","year":"1970","journal-title":"Fundamenta Mathematicae"},{"key":"S0022481200025937_ref006","volume-title":"Set theory","author":"Jech","year":"1978"},{"key":"S0022481200025937_ref004","first-page":"245","volume-title":"Contributions to the theory of games","volume":"2","author":"Gale","year":"1953"},{"key":"S0022481200025937_ref002","unstructured":"DuBose Derrick A. , Determinacy and the sharp function on objects of type k (to appear)."},{"key":"S0022481200025937_ref009","volume-title":"Descriptive set theory","author":"Moschovakis","year":"1980"},{"key":"S0022481200025937_ref001","unstructured":"DuBose Derrick A. , Determinacy and the sharp function on the reals (to appear)."},{"key":"S0022481200025937_ref007","doi-asserted-by":"publisher","DOI":"10.2307\/2372632"},{"key":"S0022481200025937_ref003","doi-asserted-by":"publisher","DOI":"10.4064\/fm-72-1-79-95"},{"key":"S0022481200025937_ref005","first-page":"685","volume":"43","author":"Harrington","year":"1978","journal-title":"Analytic determinacy and 0#"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200025937","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,18]],"date-time":"2019-05-18T17:13:46Z","timestamp":1558199626000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200025937\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,6]]},"references-count":9,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1990,6]]}},"alternative-id":["S0022481200025937"],"URL":"https:\/\/doi.org\/10.2307\/2274643","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,6]]}}}