{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,28]],"date-time":"2022-03-28T22:57:55Z","timestamp":1648508275858},"reference-count":15,"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":7497,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1993,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We investigate the connection between <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200020983_inline1\" \/>-stability for random and Cohen forcing notions and the measurability and categoricity of the <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200020983_inline1\" \/>-sets. We show that Shelah's model for <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200020983_inline1\" \/>-measurability and categoricity satisfies <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200020983_inline1\" \/>-random-stability while it does not satisfy <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200020983_inline1\" \/>-Cohen-stability. This gives an example of measure-category asymmetry. We also present a result concerning finite support iterations of Suslin forcing.<\/jats:p>","DOI":"10.2307\/2275106","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T22:49:16Z","timestamp":1146955756000},"page":"941-954","source":"Crossref","is-referenced-by-count":0,"title":["-stability"],"prefix":"10.1017","volume":"58","author":[{"given":"Dror","family":"Ben-Ari\u00e9","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haim","family":"Judah","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200020983_ref003","volume-title":"Advanced set theory","author":"Bartoszy\u0144ski"},{"key":"S0022481200020983_ref010","first-page":"1188","volume":"53","author":"Judah","year":"1988","journal-title":"Souslin forcing"},{"key":"S0022481200020983_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/BF02764965"},{"key":"S0022481200020983_ref008","first-page":"78","volume":"54","author":"Judah","year":"1989","journal-title":"Martin's axiom, measurability and equiconsistency results"},{"key":"S0022481200020983_ref014","doi-asserted-by":"publisher","DOI":"10.1007\/BF02760522"},{"key":"S0022481200020983_ref013","first-page":"957","volume":"51","author":"Pawlikowski","year":"1986","journal-title":"Why Solovay real produces Cohen real"},{"key":"S0022481200020983_ref001","volume-title":"Theory of the Continuum","author":"Bagaria","year":"1992"},{"key":"S0022481200020983_ref002","doi-asserted-by":"publisher","DOI":"10.2307\/1999530"},{"key":"S0022481200020983_ref004","volume-title":"Set theory","author":"Jech","year":"1978"},{"key":"S0022481200020983_ref005","doi-asserted-by":"publisher","DOI":"10.1017\/9781316718254.011"},{"key":"S0022481200020983_ref006","volume-title":"Archive for Mathematical Logic","author":"Judah"},{"key":"S0022481200020983_ref007","first-page":"361","article-title":"-sets: Measure and category","volume":"6","author":"Judah","year":"1993","journal-title":"Israel Mathematical Conference Proceedings"},{"key":"S0022481200020983_ref011","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1016\/0168-0072(89)90016-X","article-title":"-sets of reals","volume":"42","author":"Judah","year":"1989","journal-title":"Annals of Pure and Applied Logic"},{"key":"S0022481200020983_ref012","volume-title":"Set theory\u2014an introduction to independence proofs","author":"Kunen","year":"1980"},{"key":"S0022481200020983_ref015","volume-title":"Logic Colloquium 76","author":"Truss","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\/S0022481200020983","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,15]],"date-time":"2019-05-15T22:02:40Z","timestamp":1557957760000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200020983\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1993,9]]},"references-count":15,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1993,9]]}},"alternative-id":["S0022481200020983"],"URL":"https:\/\/doi.org\/10.2307\/2275106","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1993,9]]}}}