{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,3,15]],"date-time":"2024-03-15T11:42:35Z","timestamp":1710502955468},"reference-count":21,"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":1380,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2010,6]]},"abstract":"Abstract<\/jats:title>As is well-known, the Bernays-Sch\u00f6nfinkel-Ramsey class of all prenex \u2203*\u2200*-sentences which are valid in classical first-order logic is decidable. This paper paves the way to an analogous result which the authors deem to hold when the only available predicate symbols are \u2208 and =, no constants or function symbols are present, and one moves inside a (rather generic) Set Theory whose axioms yield the well-foundedness of membership and the existence of infinite sets. Here semi-decidability of the satisfiability problem for the BSR class is proved by following a purely semantic approach, the remaining part of the decidability result being postponed to a forthcoming paper.<\/jats:p>","DOI":"10.2178\/jsl\/1268917490","type":"journal-article","created":{"date-parts":[[2010,3,18]],"date-time":"2010-03-18T13:05:57Z","timestamp":1268917557000},"page":"459-480","source":"Crossref","is-referenced-by-count":18,"title":["The Bernays-Sch\u00f6nfinkel-Ramsey class for set theory: semidecidability"],"prefix":"10.1017","volume":"75","author":[{"given":"Eugenio","family":"Omodeo","sequence":"first","affiliation":[]},{"given":"Alberto","family":"Policriti","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200002632_ref001","volume-title":"Non-well-founded sets","volume":"14","author":"Aczel","year":"1988"},{"key":"S0022481200002632_ref005","volume-title":"Combinatorics","author":"Bollob\u00e1s","year":"1986"},{"key":"S0022481200002632_ref013","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19960420105"},{"key":"S0022481200002632_ref004","doi-asserted-by":"crossref","first-page":"55","DOI":"10.1215\/00294527-2007-003","article-title":"Decidability of \u2203*\u2200\u2200-sentences in HF","volume":"49","author":"Bell\u00e8","year":"2008","journal-title":"Notre Dame Journal of Formal Logic"},{"key":"S0022481200002632_ref020","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-97-03630-7"},{"key":"S0022481200002632_ref021","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s2-30.1.264"},{"key":"S0022481200002632_ref007","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160340203"},{"key":"S0022481200002632_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-59207-2"},{"key":"S0022481200002632_ref019","volume-title":"The satisfiability problem for the class \u2203*\u2200\u2200 in a set-theoretic setting","author":"Parlamento","year":"1992"},{"key":"S0022481200002632_ref003","first-page":"1200","volume":"71","author":"Bell\u00e8","year":"2006","journal-title":"Truth in V for \u2203*\u2200\u2200-sentences isdecidahle"},{"key":"S0022481200002632_ref008","volume-title":"Set theory for computing. 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