{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,5]],"date-time":"2023-09-05T05:14:10Z","timestamp":1693890850320},"reference-count":8,"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":11880,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1981,9]]},"abstract":"<jats:p>It is a well-known fact that two structures are \u221e<jats:italic>\u03c9<\/jats:italic>-equivalent if and only if they are isomorphic in some Boolean extension of the universe of sets (cf. [4]; an early allusion to this result appears in [8]). My principal object here is to show that arbitrary toposes defined over the category of sets may be used instead. Thus \u221e<jats:italic>\u03c9<\/jats:italic>-equivalence means isomorphism in the extremely general context of some universe of \"variable\" sets in which not only is much of the usual set-theoretic machinery unavailable but the underlying logic is not even classical. This provides further support for the view that \u221e<jats:italic>\u03c9<\/jats:italic>-equivalence is a relation between structures of fundamental importance.<\/jats:p>","DOI":"10.2307\/2273748","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:56:46Z","timestamp":1146952606000},"page":"449-459","source":"Crossref","is-referenced-by-count":1,"title":["Isomorphism of structures in <i>S<\/i>-toposes"],"prefix":"10.1017","volume":"46","author":[{"given":"J. L.","family":"Bell","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200045321_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BF02761465"},{"key":"S0022481200045321_ref001","volume-title":"Boolean-valued models and independence proofs in set theory","author":"Bell","year":"1977"},{"key":"S0022481200045321_ref005","volume-title":"A category approach to Boolean-valued set theory","author":"Higgs","year":"1973"},{"key":"S0022481200045321_ref002","unstructured":"Brockway M. , Soft objects of a topos and sheaves over the global truth values, unpublished manuscript."},{"key":"S0022481200045321_ref004","first-page":"639","volume":"41","author":"Ellentuck","year":"1976","journal-title":"Categoricity regained"},{"key":"S0022481200045321_ref003","volume-title":"Large infinitary languages","author":"Dickmann","year":"1975"},{"key":"S0022481200045321_ref007","volume-title":"Categories for the working mathematician","author":"Maclane","year":"1971"},{"key":"S0022481200045321_ref006","volume-title":"Topos theory","author":"Johstone","year":"1977"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200045321","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,25]],"date-time":"2019-05-25T19:44:10Z","timestamp":1558813450000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200045321\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1981,9]]},"references-count":8,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1981,9]]}},"alternative-id":["S0022481200045321"],"URL":"https:\/\/doi.org\/10.2307\/2273748","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1981,9]]}}}