{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T10:27:51Z","timestamp":1772447271448,"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":9050,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1989,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>No theory of a partially ordered set of finite width has the independence property, generalizing Poizat's corresponding result for linearly ordered sets. In fact, a question of Poizat concerning linearly ordered sets is answered by showing, moreover, that no theory of a partially ordered set of finite width has the multi-order property. It then follows that a distributive lattice is not finite-dimensional iff its theory has the independence property iff its theory has the multi-order property.<\/jats:p>","DOI":"10.2307\/2274855","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:30:21Z","timestamp":1146954621000},"page":"396-401","source":"Crossref","is-referenced-by-count":2,"title":["Partially ordered sets and the independence property"],"prefix":"10.1017","volume":"54","author":[{"given":"James H.","family":"Schmerl","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200027043_ref006","first-page":"1","article-title":"Decidability of second-order theories and automata on finite trees","volume":"141","author":"Rabin","year":"1969","journal-title":"Transactions of the American Mathematical Society"},{"key":"S0022481200027043_ref001","doi-asserted-by":"publisher","DOI":"10.2307\/1969503"},{"key":"S0022481200027043_ref004","first-page":"841","volume":"47","author":"Parigot","year":"1982","journal-title":"Th\u00e9ories d'arbres"},{"key":"S0022481200027043_ref005","first-page":"513","volume":"46","author":"Poizat","year":"1981","journal-title":"Th\u00e9ories instables"},{"key":"S0022481200027043_ref010","first-page":"707","article-title":"\u21350-categorical distributive lattices of finite breadth","volume":"87","author":"Schmerl","year":"1983","journal-title":"Proceedings of the American Mathematical Society"},{"key":"S0022481200027043_ref003","first-page":"481","volume":"43","author":"Keisler","year":"1978","journal-title":"The stability function of a theory"},{"key":"S0022481200027043_ref008","first-page":"101","volume":"46","author":"Schmerl","year":"1981","journal-title":"Decidability and finite axiomatizability of theories of \u21350-categorical partially ordered sets"},{"key":"S0022481200027043_ref002","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1984-0742419-0"},{"key":"S0022481200027043_ref011","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(71)90015-5"},{"key":"S0022481200027043_ref009","first-page":"269","volume-title":"Orders: description and roles (proceedings, L'Arbresle, 1982","author":"Schmerl","year":"1984"},{"key":"S0022481200027043_ref007","first-page":"585","volume":"45","author":"Schmerl","year":"1980","journal-title":"Decidability and \u21350-categoricity of theories of partially ordered sets"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200027043","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,19]],"date-time":"2019-05-19T20:26:52Z","timestamp":1558297612000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200027043\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1989,6]]},"references-count":11,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1989,6]]}},"alternative-id":["S0022481200027043"],"URL":"https:\/\/doi.org\/10.2307\/2274855","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1989,6]]}}}