{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T21:34:19Z","timestamp":1775511259407,"version":"3.50.1"},"reference-count":28,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":12245,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1980,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper is primarily concerned with \u2135<jats:sub>0<\/jats:sub>-categoricity of theories of partially ordered sets. It contains some general conjectures, a collection of known results and some new theorems on \u2135<jats:sub>0<\/jats:sub>-categoricity. Among the latter are the following.<\/jats:p><jats:p>Corollary 3.3. <jats:italic>For every countable<\/jats:italic> \u2135<jats:sub>0<\/jats:sub>-<jats:italic>categorical<\/jats:italic><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200046569_inline1\"\/><jats:italic>there is a linear order of A such that<\/jats:italic> (<jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200046569_inline1\"\/>, &lt;) <jats:italic>is<\/jats:italic> \u2135<jats:sub>0<\/jats:sub>-<jats:italic>categorical<\/jats:italic>.<\/jats:p><jats:p>Corollary 6.7. <jats:italic>Every<\/jats:italic> \u2135<jats:sub>0<\/jats:sub>-<jats:italic>categorical theory of a partially ordered set of finite width has a decidable theory<\/jats:italic>.<\/jats:p><jats:p>Theorem 7.7. <jats:italic>Every<\/jats:italic> \u2135<jats:sub>0<\/jats:sub>-<jats:italic>categorical theory of reticles has a decidable theory<\/jats:italic>.<\/jats:p><jats:p>There is a section dealing just with decidability of partially ordered sets, the main result of this section being<\/jats:p><jats:p>Theorem 8.2. <jats:italic>If (P, &lt;) is a finite partially ordered set and K<jats:sub>P<\/jats:sub> is the class of partially ordered sets which do not embed (P, &lt;), then<\/jats:italic> Th(<jats:italic>K<jats:sub>P<\/jats:sub><\/jats:italic>) <jats:italic>is decidable iff K<jats:sub>P<\/jats:sub> contains only reticles<\/jats:italic>.<\/jats:p>","DOI":"10.2307\/2273425","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T17:53:41Z","timestamp":1146938021000},"page":"585-611","source":"Crossref","is-referenced-by-count":11,"title":["Decidability and \u2135<sub>0<\/sub>-categoricity of theories of partially ordered sets"],"prefix":"10.1017","volume":"45","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":"S0022481200046569_ref022","first-page":"545","article-title":"On the categoricity in power \u2264 \u21350","volume":"7","author":"Ryll-Nardzewski","year":"1959","journal-title":"Bulletin de l'Acad\u00e9mie Polonaise des Sciences. 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