{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,5]],"date-time":"2025-11-05T06:09:59Z","timestamp":1762322999522},"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":3206,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2005,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The lexicographic power \u0394<jats:sup>\u0393<\/jats:sup> of chains \u0394 and \u0393 is, roughly, the Cartesian power \u03a0<jats:sub>\u03b3\u0404\u0393<\/jats:sub>\u0394 totally ordered lexicographically from the left. Here the focus is on certain powers in which either \u0394 = \u211d or \u211a = \u211d, with emphasis on when two such powers are isomorphic and on when \u0394<jats:sup>\u0393<\/jats:sup> is 2-homogeneous. The main results are:<\/jats:p><jats:p>(1) For a countably infinite ordinal <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200006988_inline1\" \/><\/jats:p><jats:p>(2) \u211d<jats:sup>\u211d<\/jats:sup> \u2244 \u211d<jats:sup>\u211a<\/jats:sup>.<\/jats:p><jats:p>(3) For \u0394 a countable ordinal \u2265 2, \u0394<jats:sup>\u211d<\/jats:sup> with its smallest element deleted, is 2-homogeneous.<\/jats:p>","DOI":"10.2178\/jsl\/1120224719","type":"journal-article","created":{"date-parts":[[2005,7,1]],"date-time":"2005-07-01T11:01:40Z","timestamp":1120215700000},"page":"389-409","source":"Crossref","is-referenced-by-count":4,"title":["Lexicographic exponentiation of chains"],"prefix":"10.1017","volume":"70","author":[{"given":"W. C.","family":"Holland","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S.","family":"Kuhlmann","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"S. H.","family":"McCleary","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200006988_ref011","unstructured":"Warton P. , Lexicographic powers of the real line, Ph. D. Dissertation, Bowling Green State University, 1998."},{"key":"S0022481200006988_ref009","unstructured":"Kuhlmann S. and Shklah S. , \u03ba-hounded exponential-logarithmic power series fields, 2004, submitted."},{"key":"S0022481200006988_ref007","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1995-1260172-4"},{"key":"S0022481200006988_ref001","volume-title":"Partially ordered algebraic systems","author":"Fuchs","year":"1963"},{"key":"S0022481200006988_ref002","unstructured":"Green T. , Properties of chain products and Ehrenfeucht-Fra\u00efss\u00e9 games on chains, Msc. Thesis, University of Saskatchewan, 08 2002."},{"key":"S0022481200006988_ref008","volume-title":"Ordered exponential fields","volume":"12","author":"Kuhlmann","year":"2000"},{"key":"S0022481200006988_ref010","volume-title":"Linear orderings","author":"Rosknstein","year":"1982"},{"key":"S0022481200006988_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BF01451165"},{"key":"S0022481200006988_ref004","volume-title":"Grundz\u00fcge der Mengenlehre","author":"Hausdoff","year":"1914"},{"key":"S0022481200006988_ref005","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-97-03964-6"},{"key":"S0022481200006988_ref006","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-03-06830-8"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200006988","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,3]],"date-time":"2019-05-03T16:50:01Z","timestamp":1556902201000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200006988\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,6]]},"references-count":11,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2005,6]]}},"alternative-id":["S0022481200006988"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1120224719","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,6]]}}}