{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T05:41:09Z","timestamp":1648791669646},"reference-count":6,"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":8685,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1990,6]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this note we prove that the abstract property \u201cweakly subdirectly indecomposable\u201d does not characterize the class IWs<jats:sub>\u03b1<\/jats:sub> of weak cylindric set algebras. However, we give another (similar) abstract property characterizing IWs<jats:sub>\u03b1<\/jats:sub>. The original property does characterize the directed unions of members of IWs<jats:sub>\u03b1<\/jats:sub> iff \u03b1 is countable. Free algebras will be shown to satisfy the original property.<\/jats:p>","DOI":"10.2307\/2274648","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:35:29Z","timestamp":1146954929000},"page":"577-588","source":"Crossref","is-referenced-by-count":3,"title":["Weak cylindric set algebras and weak subdirect indecomposability"],"prefix":"10.1017","volume":"55","author":[{"given":"H.","family":"Andr\u00e9ka","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"I.","family":"N\u00e9meti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"R. J.","family":"Thompson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200025986_ref001","unstructured":"Andr\u00e9ka H. and N\u00e9meti I. , IWs\u03b1 is not characterized by weak subdirect indecomposability and is not closed under directed unions either, preprint, 1983."},{"key":"S0022481200025986_ref006","doi-asserted-by":"crossref","unstructured":"Henkin L. , Monk J. D. and Tarski A. , Cylindric set algebras and related structures, in [HMTAN], pp. 1\u2013129.","DOI":"10.1007\/BFb0095613"},{"key":"S0022481200025986_ref003","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0095613"},{"key":"S0022481200025986_ref002","volume-title":"Algebraic logic (proceedings, Budapest, 1988)","author":"Goldblatt"},{"key":"S0022481200025986_ref004","volume-title":"Cylindric algebras","author":"Henkin","year":"1971"},{"key":"S0022481200025986_ref005","volume-title":"Cylindric algebras","author":"Henkin","year":"1985"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200025986","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,18]],"date-time":"2019-05-18T21:13:39Z","timestamp":1558214019000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200025986\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1990,6]]},"references-count":6,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1990,6]]}},"alternative-id":["S0022481200025986"],"URL":"https:\/\/doi.org\/10.2307\/2274648","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1990,6]]}}}