{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,5]],"date-time":"2022-04-05T03:02:20Z","timestamp":1649127740926},"reference-count":7,"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>Let <jats:italic>\u03b2<\/jats:italic> be an arbitrary limit ordinal. A <jats:italic>\u03b2<\/jats:italic>-r.e. set is <jats:italic>l<\/jats:italic>-finite iff all its <jats:italic>\u03b2<\/jats:italic>-r.e. subsets are <jats:italic>\u03b2<\/jats:italic>-recursive. The <jats:italic>l<\/jats:italic>-finite sets correspond to the ideal of finite sets in the lattice of r.e. sets. We give a characterization of <jats:italic>l<\/jats:italic>-finite sets in terms of their ordertype: a <jats:italic>\u03b2<\/jats:italic>-r.e. set is <jats:italic>l<\/jats:italic>-finite iff it has ordertype less than <jats:italic>\u03b2<\/jats:italic>*, the <jats:italic>\u03a3<\/jats:italic><jats:sub>1<\/jats:sub>, projectum of <jats:italic>\u03b2<\/jats:italic>).<\/jats:p>","DOI":"10.2307\/2274647","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:35:29Z","timestamp":1146954929000},"page":"573-576","source":"Crossref","is-referenced-by-count":0,"title":["The ordertype of <i>\u03b2<\/i>-R.E. sets"],"prefix":"10.1017","volume":"55","author":[{"given":"Klaus","family":"Sutner","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200025974_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0059290"},{"key":"S0022481200025974_ref006","unstructured":"Sutner K. , Lattices of \u03b2-r.e. sets (to appear)."},{"key":"S0022481200025974_ref002","first-page":"405","volume":"41","author":"Lerman","year":"1976","journal-title":"Congruence relations, filters, ideals and definability in lattices of \u03b1-r.e. sets"},{"key":"S0022481200025974_ref007","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(81)90015-2"},{"key":"S0022481200025974_ref004","first-page":"173","article-title":"\u03b2-recursion theory","volume":"255","author":"Friedman","year":"1979","journal-title":"Transactions of the American Mathematical Society"},{"key":"S0022481200025974_ref003","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19760220145"},{"key":"S0022481200025974_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(80)90042-0"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200025974","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,18]],"date-time":"2019-05-18T21:13:56Z","timestamp":1558214036000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200025974\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,6]]},"references-count":7,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1990,6]]}},"alternative-id":["S0022481200025974"],"URL":"https:\/\/doi.org\/10.2307\/2274647","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,6]]}}}