{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T12:57:19Z","timestamp":1772456239409,"version":"3.50.1"},"reference-count":11,"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>We provide partial answers to the following problem: Is the class of Borel linear orders well-quasi-ordered under embeddability? We show that it is indeed the case for those Borel orders which are embeddable in <jats:bold>R<\/jats:bold><jats:sup>\u03c9<\/jats:sup>, with the lexicographic ordering. For Borel orders embeddable in <jats:bold>R<\/jats:bold><jats:sup>2<\/jats:sup>, our proof works in ZFC, but it uses projective determinacy for Borel orders embeddable in some <jats:bold>R<jats:sup><jats:italic>n<\/jats:italic><\/jats:sup><\/jats:bold>, <jats:italic>n<\/jats:italic> &lt; \u03c9, and hyperprojective determinacy for the general case.<\/jats:p>","DOI":"10.2307\/2274645","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:35:29Z","timestamp":1146940529000},"page":"537-560","source":"Crossref","is-referenced-by-count":13,"title":["On the quasi-ordering of Borel linear orders under embeddability"],"prefix":"10.1017","volume":"55","author":[{"given":"Alain","family":"Louveau","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jean","family":"Saint-Raymond","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200025950_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(81)90001-2"},{"key":"S0022481200025950_ref001","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1940-07213-1"},{"key":"S0022481200025950_ref004","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1988-0965754-3"},{"key":"S0022481200025950_ref008","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100039062"},{"key":"S0022481200025950_ref009","doi-asserted-by":"publisher","DOI":"10.1017\/S030500410004281X"},{"key":"S0022481200025950_ref006","first-page":"865","volume":"54","author":"Louveau","year":"1989","journal-title":"Two results on Borel orders"},{"key":"S0022481200025950_ref002","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/065\/891249"},{"key":"S0022481200025950_ref011","unstructured":"Woodin W. H. , private communication."},{"key":"S0022481200025950_ref005","doi-asserted-by":"publisher","DOI":"10.2307\/1970754"},{"key":"S0022481200025950_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0071696"},{"key":"S0022481200025950_ref010","first-page":"124","volume-title":"Recursive aspects of descriptive set theory","volume":"11","author":"Simpson","year":"1985"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200025950","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,18]],"date-time":"2019-05-18T17:13:20Z","timestamp":1558199600000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200025950\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,6]]},"references-count":11,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1990,6]]}},"alternative-id":["S0022481200025950"],"URL":"https:\/\/doi.org\/10.2307\/2274645","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,6]]}}}