{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,8,31]],"date-time":"2023-08-31T04:57:57Z","timestamp":1693457877899},"reference-count":7,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":16110,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1970,2]]},"abstract":"<jats:p>In this paper we consider some axiomatic systems of set theory related to the system NF (New Foundations) of Quine. In particular we discuss the possible relations of cardinality between a finite set <jats:italic>x<\/jats:italic> and its subset class SC(x) = {<jats:italic>y<\/jats:italic> | <jats:italic>y<\/jats:italic> \u2229 x} and also between <jats:italic>x<\/jats:italic> and its unit set class USC(x) = {{<jats:italic>y<\/jats:italic>} | y \u03b5 x}. Specker [5] has shown that in NF the cardinal of a finite set <jats:italic>x<\/jats:italic> can never be the same as the cardinal of SC(<jats:italic>x<\/jats:italic>).<\/jats:p>","DOI":"10.2307\/2270852","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T20:57:14Z","timestamp":1146949034000},"page":"589-596","source":"Crossref","is-referenced-by-count":4,"title":["Finite sets in Quine's new foundations"],"prefix":"10.1017","volume":"34","author":[{"given":"C.","family":"Ward Henson","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200093166_ref001","doi-asserted-by":"publisher","DOI":"10.4064\/fm-43-1-50-68"},{"key":"S0022481200093166_ref004","volume-title":"Logic for mathematicians","author":"Rosser","year":"1953"},{"key":"S0022481200093166_ref007","first-page":"644","article-title":"Review of [1]","volume":"31","author":"Vaught","year":"1966","journal-title":"this Journal"},{"key":"S0022481200093166_ref006","first-page":"116","volume-title":"Logic, methodology and philosophy of science","author":"Specker","year":"1962"},{"key":"S0022481200093166_ref003","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-64-03163-1"},{"key":"S0022481200093166_ref005","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.39.9.972"},{"key":"S0022481200093166_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/BF00568059"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200093166","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,22]],"date-time":"2023-03-22T10:36:05Z","timestamp":1679481365000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200093166\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1970,2]]},"references-count":7,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1970,2]]}},"alternative-id":["S0022481200093166"],"URL":"https:\/\/doi.org\/10.2307\/2270852","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1970,2]]}}}