{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T08:04:31Z","timestamp":1775462671370,"version":"3.50.1"},"reference-count":3,"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":17543,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1966,3]]},"abstract":"<jats:p>In this paper we follow up our work in [2] on standard classes of recursively enumerable sets, and it will be supposed that the reader is familiar with [2]. One of the main problems left open in [2], that of determining whether or not every standard class has a least member is resolved by the construction of a standard class all of whose members are non-empty, and two of whose members are disjoint. This shows that there is a standard class which is not p.r. in the sense of [2] and we now prefer the adjective <jats:italic>sequential<\/jats:italic> for those standard classes which were called p.r. in [2]. Otherwise our terminology will be the same as in [2]. We shall also prove the theorem only stated in [2] that any standard class all of whose members have cardinality &lt; 3 is sequential. Further, we give an example of a standard class which is not sequential and all of whose members have cardinality &lt; 4.<\/jats:p>","DOI":"10.2307\/2270617","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T16:31:27Z","timestamp":1146933087000},"page":"10-22","source":"Crossref","is-referenced-by-count":16,"title":["On the indexing of classes of recursively enumerable sets"],"prefix":"10.1017","volume":"31","author":[{"given":"A. H.","family":"Lachlan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200067992_ref002","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19640100203"},{"key":"S0022481200067992_ref003","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19550010205"},{"key":"S0022481200067992_ref001","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19610071108"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200067992","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,2]],"date-time":"2019-06-02T17:10:48Z","timestamp":1559495448000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200067992\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1966,3]]},"references-count":3,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1966,3]]}},"alternative-id":["S0022481200067992"],"URL":"https:\/\/doi.org\/10.2307\/2270617","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1966,3]]}}}