{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,30]],"date-time":"2024-03-30T22:40:45Z","timestamp":1711838445044},"reference-count":12,"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":1197,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2010,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>An instance of Stratified Comprehension<\/jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0022481200002267_eqnU1\" \/><\/jats:disp-formula><\/jats:p><jats:p>is called<jats:italic>strictly impredicative<\/jats:italic>iff, under minimal stratification, the type of<jats:italic>x<\/jats:italic>is 0. Using the technology of forcing, we prove that the fragment of<jats:bold>NF<\/jats:bold>based on strictly impredicative Stratified Comprehension is consistent. A crucial part in this proof, namely showing genericity of a certain symmetric filter, is due to Robert Solovay.<\/jats:p><jats:p>As a bonus, our interpretation also satisfies some instances of Stratified Comprehension which are<jats:italic>not<\/jats:italic>strictly impredicative. For example, it verifies existence of Frege natural numbers.<\/jats:p><jats:p>Apparently, this is a new subsystem of<jats:bold>NF<\/jats:bold>shown to be consistent. The consistency question for the whole theory<jats:bold>NF<\/jats:bold>remains open (since 1937).<\/jats:p>","DOI":"10.2178\/jsl\/1286198149","type":"journal-article","created":{"date-parts":[[2010,10,4]],"date-time":"2010-10-04T13:16:13Z","timestamp":1286198173000},"page":"1326-1338","source":"Crossref","is-referenced-by-count":0,"title":["Consistency of strictly impredicative NF and a little more \u2026"],"prefix":"10.1017","volume":"75","author":[{"given":"Sergei","family":"Tupailo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200002267_ref003","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198514770.001.0001","volume-title":"Set theory with a universal set","author":"Forster","year":"1995"},{"key":"S0022481200002267_ref006","volume-title":"Set theory","author":"Jech","year":"2002"},{"key":"S0022481200002267_ref005","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1305\/ndjfl\/1038949535","article-title":"Subsystems of Quine's \u201cNew Foundations\u201d with predicativity restrictions","volume":"40","author":"Holmes","year":"1999","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"S0022481200002267_ref009","doi-asserted-by":"publisher","DOI":"10.1080\/00029890.1937.11987928"},{"key":"S0022481200002267_ref012","first-page":"99","volume-title":"Proceedings of the 70th anniversary NF meeting in Cambridge","volume":"16","author":"Tupailo","year":"2009"},{"key":"S0022481200002267_ref008","volume-title":"Set theory. An introduction to independence proofs","author":"Kunen","year":"1980"},{"key":"S0022481200002267_ref001","first-page":"102","article-title":"ZFJ and the consistency problem for NF","volume":"1","author":"Boffa","year":"1988","journal-title":"Jahrbuch der Kurt G\u00f6del Gesellschaft"},{"key":"S0022481200002267_ref002","first-page":"131","volume":"47","author":"Crabb\u00e9","year":"1982","journal-title":"On the consistency of an impredicative subsystem of Quine's NF"},{"key":"S0022481200002267_ref011","first-page":"255","volume-title":"Proceedings of logic Colloquium 2005","volume":"28","author":"Tupailo","year":"2008"},{"key":"S0022481200002267_ref004","first-page":"1","volume":"9","author":"Hailperin","year":"1944","journal-title":"A set of axioms for logic"},{"key":"S0022481200002267_ref007","doi-asserted-by":"publisher","DOI":"10.1007\/BF00568059"},{"key":"S0022481200002267_ref010","first-page":"116","volume-title":"Logic, Methodology and Philosophy of Science","author":"Specker","year":"1962"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200002267","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,3,30]],"date-time":"2024-03-30T22:24:24Z","timestamp":1711837464000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200002267\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,12]]},"references-count":12,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2010,12]]}},"alternative-id":["S0022481200002267"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1286198149","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,12]]}}}