{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,6]],"date-time":"2026-04-06T13:52:36Z","timestamp":1775483556347,"version":"3.50.1"},"reference-count":7,"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":14072,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1975,9]]},"abstract":"<jats:p>In [3] we have associated to a structure an ordinal which gives us information about elementary substructures of the structure. For example a structure whose ascending chain number (as we call the ordinal) is <jats:italic>\u03c9<\/jats:italic> could be called Noetherian since all ascending elementary chains inside it are finite (and there are arbitrarily large finite chains). Theorem 2 shows that such structures exist. In fact we prove that for any <jats:italic>\u03b1<\/jats:italic> &lt; <jats:italic>\u03c9<\/jats:italic><jats:sub>1<\/jats:sub> there is a structure whose ascending chain number is <jats:italic>\u03b1<\/jats:italic>. The construction is based on the existence of a certain group of permutations of <jats:italic>\u03c9<\/jats:italic> (see Theorem 1). The second part of this paper deals with the relevance of the chain number to the study of Jonsson algebras.<\/jats:p>","DOI":"10.2307\/2272160","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:36:35Z","timestamp":1146951395000},"page":"383-388","source":"Crossref","is-referenced-by-count":1,"title":["Construction of models from groups of permutations"],"prefix":"10.1017","volume":"40","author":[{"given":"Miroslav","family":"Benda","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S002248120005297X_ref007","first-page":"81","article-title":"Arithmetical extensions of relational systems","volume":"13","author":"Tarski","year":"1957","journal-title":"Compositio Mathematica"},{"key":"S002248120005297X_ref006","first-page":"439","volume":"36","author":"Rosenstein","year":"1971","journal-title":"A note on a theorem of Vaught"},{"key":"S002248120005297X_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/BF02771623"},{"key":"S002248120005297X_ref003","volume-title":"Mathematica Scandinavica","author":"Benda"},{"key":"S002248120005297X_ref002","doi-asserted-by":"publisher","DOI":"10.4064\/fm-81-2-107-119"},{"key":"S002248120005297X_ref001","first-page":"79","volume":"36","author":"Baldwin","year":"1971","journal-title":"On strongly minimal sets"},{"key":"S002248120005297X_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF02771624"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S002248120005297X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T19:21:46Z","timestamp":1559157706000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S002248120005297X\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1975,9]]},"references-count":7,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1975,9]]}},"alternative-id":["S002248120005297X"],"URL":"https:\/\/doi.org\/10.2307\/2272160","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1975,9]]}}}