{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T02:07:34Z","timestamp":1648778854002},"reference-count":9,"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":16358,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1969,5,29]]},"abstract":"<jats:p>In this paper a special type of co-ordinal, called rich, is studied. Basic properties of rich co-ordinals are proved in \u00a71. In \u00a72 rich co-ordinals are seen to be the co-ordinals occurring in paths which are addition isomorphic to initial segments of the classical ordinals. The results of \u00a71 are applied to obtain information about and examples of such paths. In the next section the order types of rich co-ordinals with a given field, <jats:italic>X<\/jats:italic>, is seen to be determined essentially by the finite divisors of <jats:italic>X<\/jats:italic>. RETs satisfying various divisibility conditions are constructed in \u00a74.<\/jats:p>","DOI":"10.2307\/2270980","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T20:52:03Z","timestamp":1146948723000},"page":"45-52","source":"Crossref","is-referenced-by-count":0,"title":["Rich co-ordinals, addition isomorphisms, and RETs"],"prefix":"10.1017","volume":"34","author":[{"given":"Alfred B.","family":"Manaster","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200095062_ref004","first-page":"67","article-title":"Recursive equivalence types","volume":"3","author":"Dekker","year":"1960","journal-title":"University of California Publications in Mathematics (New Series)"},{"key":"S0022481200095062_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BF01362769"},{"key":"S0022481200095062_ref001","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71691-4"},{"key":"S0022481200095062_ref007","unstructured":"Manaster A. B. , Full co-ordinals of RETs, Pacific Journal of Mathematics (to appear)."},{"key":"S0022481200095062_ref002","first-page":"525","article-title":"Constructive order types. II","volume":"31","author":"Crossley","year":"1966","journal-title":"this Journal"},{"key":"S0022481200095062_ref009","volume-title":"Polska Akademia Nauk","author":"Sierpinski","year":"1958"},{"key":"S0022481200095062_ref006","doi-asserted-by":"crossref","unstructured":"Manaster A. B. , Higher-order indecomposable isols, Ph.D. thesis, Cornell University, 1965.","DOI":"10.2307\/1994569"},{"key":"S0022481200095062_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BF01558589"},{"key":"S0022481200095062_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/BF01211004"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200095062","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,1]],"date-time":"2019-06-01T20:13:58Z","timestamp":1559420038000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200095062\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1969,5,29]]},"references-count":9,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1969,5,29]]}},"alternative-id":["S0022481200095062"],"URL":"https:\/\/doi.org\/10.2307\/2270980","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1969,5,29]]}}}