{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T18:39:21Z","timestamp":1648838361725},"reference-count":6,"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":8777,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1990,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>C. Karp has shown that if \u03b1 is an ordinal with <jats:italic>\u03c9<\/jats:italic><jats:sup>\u03b1<\/jats:sup> = \u03b1 and <jats:italic>A<\/jats:italic> is a linear ordering with a smallest element, then \u03b1 and \u03b1 \u2297 <jats:italic>A<\/jats:italic> are equivalent in <jats:italic>L<\/jats:italic><jats:sub>\u221e<jats:italic>\u03c9<\/jats:italic><\/jats:sub> up to quantifer rank \u03b1. This result can be expressed in terms of Ehrenfeucht-Fra\u00efss\u00e9 games where player \u2200 has to make additional moves by choosing elements of a descending sequence in \u03b1. Our aim in this paper is to prove a similar result for Ehrenfeucht-Fra\u00efss\u00e9 games of length <jats:italic>\u03c9<\/jats:italic><jats:sub>1<\/jats:sub>. One implication of such a result will be that a certain infinite quantifier language cannot say that a linear ordering has no descending <jats:italic>\u03c9<\/jats:italic><jats:sub>1<\/jats:sub>-sequences (when the alphabet contains only one binary relation symbol). Connected work is done by Hyttinen and Oikkonen in [H] and [O].<\/jats:p>","DOI":"10.2307\/2274954","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:33:48Z","timestamp":1146954828000},"page":"65-73","source":"Crossref","is-referenced-by-count":2,"title":["On Ehrenfeucht-Fra\u00efss\u00e9 equivalence of linear orderings"],"prefix":"10.1017","volume":"55","author":[{"given":"Juha","family":"Oikkonen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200026438_ref005","volume-title":"Annates Academiae Scientiarum Fennicae, Series A I: Mathematica. Dissertationes","author":"Karttunen","year":"1984"},{"key":"S0022481200026438_ref002","volume-title":"Fundament a Mathematicae","author":"Hyttinen"},{"key":"S0022481200026438_ref006","first-page":"175","volume-title":"Logic Colloquium '86","author":"Oikkonen","year":"1988"},{"key":"S0022481200026438_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-7798-3_4"},{"key":"S0022481200026438_ref003","unstructured":"Hyttinen T. and V\u00e4\u00e4n\u00e4nen J. , On Scott-trees of uncountable models (to appear)."},{"key":"S0022481200026438_ref004","first-page":"407","volume-title":"The theory of models","author":"Karp","year":"1965"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200026438","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,18]],"date-time":"2019-05-18T21:52:43Z","timestamp":1558216363000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200026438\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,3]]},"references-count":6,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1990,3]]}},"alternative-id":["S0022481200026438"],"URL":"https:\/\/doi.org\/10.2307\/2274954","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,3]]}}}