{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,17]],"date-time":"2023-11-17T16:03:53Z","timestamp":1700237033902},"reference-count":4,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":3238,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1998,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This note investigates the class of finite initial segments of the cumulative hierarchy of pure sets. We show that this class is first\u2010order definable over the class of finite directed graphs and that this class admits a first\u2010order definable global linear order. We apply this last result to show that FO(&lt;, BIT) = FO(BIT).<\/jats:p>","DOI":"10.1002\/malq.19980440306","type":"journal-article","created":{"date-parts":[[2007,5,30]],"date-time":"2007-05-30T22:47:06Z","timestamp":1180565226000},"page":"349-353","source":"Crossref","is-referenced-by-count":12,"title":["Elementary Properties of the Finite Ranks"],"prefix":"10.1002","volume":"44","author":[{"given":"Anuj","family":"Dawar","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kees","family":"Doets","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Steven","family":"Lindell","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Scott","family":"Weinstein","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-11035-5"},{"key":"e_1_2_1_3_2","series-title":"Proc. AMS Symp. in Appl. Math. 38","first-page":"73","volume-title":"Computational Complexity Theory","author":"Immerman N.","year":"1989"},{"key":"e_1_2_1_4_2","volume-title":"Set Theory","author":"Kunen K.","year":"1980"},{"key":"e_1_2_1_5_2","first-page":"569","article-title":"Impossibility of an algorithm for the decision problem in finite classes","volume":"70","author":"Trakhtenbrot B.","year":"1950","journal-title":"Doklady Akademii Nauk SSSR"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19980440306","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19980440306","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,29]],"date-time":"2023-10-29T00:50:10Z","timestamp":1698540610000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19980440306"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998,1]]},"references-count":4,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1998,1]]}},"alternative-id":["10.1002\/malq.19980440306"],"URL":"https:\/\/doi.org\/10.1002\/malq.19980440306","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1998,1]]}}}