{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,5,3]],"date-time":"2023-05-03T22:51:16Z","timestamp":1683154276847},"reference-count":3,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":6279,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1997,1]]},"abstract":"<jats:p>In this paper we continue the investigations begun in [2] of equivalence classes of (denumerable) well-orderings under one-one partial recursive, order-preserving maps (recursive isotonisms). The numbering and notation are continued from [2] except that we now use lower case Greek letters for classical ordinals and upper case Roman letters for sets and we slightly modify the definition of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200065968_inline1\" \/> (see \u00a7IX.3).<\/jats:p><jats:p>In section IX, after proving some lemmata which we use repeatedly in this paper, we establish the existence of Cantor Normal Forms for all co-ordinals less than a co-ordinal of the form W<jats:sup>A<\/jats:sup> (<jats:italic>a fortiori<\/jats:italic> for all co-ordinals less than a principal number for exponentiation).<\/jats:p>","DOI":"10.2307\/2269687","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T20:36:19Z","timestamp":1146947779000},"page":"525-538","source":"Crossref","is-referenced-by-count":3,"title":["Constructive order types, II"],"prefix":"10.1017","volume":"31","author":[{"given":"John N.","family":"Crossley","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200065968_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71691-4"},{"key":"S0022481200065968_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-52756-2"},{"key":"S0022481200065968_ref003","first-page":"308","article-title":"On isomorphisms of recursive well-orderings","volume":"28","author":"Crossley","journal-title":"this Journal"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200065968","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,12]],"date-time":"2019-05-12T19:40:52Z","timestamp":1557690052000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200065968\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,1]]},"references-count":3,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1966,12]]}},"alternative-id":["S0022481200065968"],"URL":"https:\/\/doi.org\/10.2307\/2269687","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997,1]]}}}