{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,5,16]],"date-time":"2022-05-16T00:26:12Z","timestamp":1652660772326},"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":13525,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1977,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let \u2133 be a structure for a language \u2112 on a set <jats:italic>M<\/jats:italic> of urelements. HYP(\u2133) is the least admissible set above \u2133. In \u00a71 we show that <jats:italic>pp<\/jats:italic>(HYP(\u2133)) [= the collection of pure sets in HYP(\u2133)] is determined in a simple way by the ordinal \u03b1 = \u00b0 (HYP(\u2133)) and the \u2112<jats:sub>x\u03c9<\/jats:sub> theory of \u2133 up to quantifier rank \u03b1. In \u00a72 we consider the question of which pure countable admissible sets are of the form <jats:italic>pp<\/jats:italic>(HYP(\u2133)) for some \u2133 and show that all sets <jats:italic>L<\/jats:italic><jats:sub>\u03b1<\/jats:sub> (\u03b1 admissible) are of this form. Other positive and negative results on this question are obtained.<\/jats:p>","DOI":"10.2307\/2272316","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T17:43:28Z","timestamp":1146937408000},"page":"33-46","source":"Crossref","is-referenced-by-count":2,"title":["The pure part of HYP(\u2133)"],"prefix":"10.1017","volume":"42","author":[{"given":"Mark","family":"Nadel","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jonathan","family":"Stavi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200050751_ref009","unstructured":"Schlipf J. , Some hyperelementary aspects of model theory, Ph.D. Thesis, University of Wisconsin, 05 1975."},{"key":"S0022481200050751_ref006","first-page":"76","volume-title":"Memoirs of the American Mathematical Society","author":"L\u00e9vy","year":"1965"},{"key":"S0022481200050751_ref005","first-page":"152","volume-title":"Lectures Notes in Mathematics","volume":"72","author":"Kueker","year":"1968"},{"key":"S0022481200050751_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/BF02758130"},{"key":"S0022481200050751_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-11035-5"},{"key":"S0022481200050751_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(74)90017-5"},{"key":"S0022481200050751_ref010","volume-title":"Subsystems of analysis","author":"Simpson","year":"1973"},{"key":"S0022481200050751_ref004","first-page":"407","volume-title":"The theory of models","author":"Karp","year":"1965"},{"key":"S0022481200050751_ref003","doi-asserted-by":"publisher","DOI":"10.4064\/fm-82-2-143-152"},{"key":"S0022481200050751_ref002","first-page":"539","volume-title":"Lecture Notes in Mathematics","volume":"337","author":"Friedman"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200050751","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,28]],"date-time":"2019-05-28T15:22:26Z","timestamp":1559056946000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200050751\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1977,3]]},"references-count":10,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1977,3]]}},"alternative-id":["S0022481200050751"],"URL":"https:\/\/doi.org\/10.2307\/2272316","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1977,3]]}}}