{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,2]],"date-time":"2022-04-02T12:20:28Z","timestamp":1648902028151},"reference-count":10,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":12795,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1979,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>If <jats:italic>A<\/jats:italic> is an admissible set, let <jats:italic>HC<\/jats:italic>(<jats:italic>A<\/jats:italic>) = {<jats:italic>x<\/jats:italic>\u2223<jats:italic>x<\/jats:italic> \u2208 <jats:italic>A<\/jats:italic> and <jats:italic>x<\/jats:italic> is hereditarily countable in <jats:italic>A<\/jats:italic>}. Then <jats:italic>HC<\/jats:italic>(<jats:italic>A<\/jats:italic>) is admissible. Corollaries are drawn characterizing the \u201creal parts\u201d of admissible sets and the analytical consequences of admissible set theory.<\/jats:p>","DOI":"10.2307\/2273707","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:49:34Z","timestamp":1146952174000},"page":"95-102","source":"Crossref","is-referenced-by-count":0,"title":["HC of an admissible set"],"prefix":"10.1017","volume":"44","author":[{"given":"Sy D.","family":"Friedman","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200048751_ref004","first-page":"107","article-title":"Functional interpretation of bar induction by bar recursion","volume":"20","author":"Howard","year":"1968","journal-title":"Compositio Mathematics"},{"key":"S0022481200048751_ref008","volume-title":"Generalized recursion theory","author":"Sacks","year":"1974"},{"key":"S0022481200048751_ref010","unstructured":"Steel J. , Subsystems of analysis and the axiom of determinacy, Ph.D. Thesis University of California, Berkeley, 1977."},{"key":"S0022481200048751_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-11035-5"},{"key":"S0022481200048751_ref007","unstructured":"Platek R. , Foundations of recursion theory, Ph.D. Thesis, University of Stanford, 1965."},{"key":"S0022481200048751_ref006","volume-title":"Mathematical logic and the foundations of set theory","author":"L\u00e9vy","year":"1970"},{"key":"S0022481200048751_ref005","first-page":"325","volume":"31","author":"Howard","year":"1966","journal-title":"Transfinite induction and bar induction of types zero and one"},{"key":"S0022481200048751_ref003","first-page":"353","volume":"34","author":"Friedman","year":"1969","journal-title":"Bar-induction and \u03a011-CA"},{"key":"S0022481200048751_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/BF02798679"},{"key":"S0022481200048751_ref009","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(76)90187-0"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200048751","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,26]],"date-time":"2019-05-26T21:56:57Z","timestamp":1558907817000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200048751\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1979,3]]},"references-count":10,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1979,3]]}},"alternative-id":["S0022481200048751"],"URL":"https:\/\/doi.org\/10.2307\/2273707","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1979,3]]}}}