{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T02:16:32Z","timestamp":1772504192164,"version":"3.50.1"},"reference-count":9,"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":4119,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2002,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>T<\/jats:italic> be an <jats:italic>\u03c9<\/jats:italic><jats:sub>1<\/jats:sub>-Souslin tree. We show the property of forcing notions; \u201cis {<jats:italic>\u03c9<\/jats:italic><jats:sub>1<\/jats:sub>}-semi-proper and preserves <jats:italic>T<\/jats:italic>\u201d is preserved by a new kind of revised countable support iteration of arbitrary length. As an application we have a forcing axiom which is compatible with the existence of an <jats:italic>\u03c9<\/jats:italic><jats:sub>1<\/jats:sub> -Souslin tree for preorders as wide as possible.<\/jats:p>","DOI":"10.2178\/jsl\/1190150293","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T19:16:54Z","timestamp":1197573414000},"page":"1431-1468","source":"Crossref","is-referenced-by-count":6,"title":["On iterating semiproper preorders"],"prefix":"10.1017","volume":"67","author":[{"given":"Tadatoshi","family":"Miyamoto","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200009154_ref004","volume-title":"Studies in logic and the foundations of mathematics","volume":"102","author":"Kunen","year":"1980"},{"key":"S0022481200009154_ref001","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0098398"},{"key":"S0022481200009154_ref002","volume-title":"Surveys in set theory","volume":"87","author":"Devlin","year":"1983"},{"key":"S0022481200009154_ref003","unstructured":"Donder H. and Fuchs U. , Handbook of set theory, To appear."},{"key":"S0022481200009154_ref009","volume-title":"Perspectives in mathematical logic","author":"Shelah","year":"1998"},{"key":"S0022481200009154_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/BF01409967"},{"key":"S0022481200009154_ref007","volume-title":"Lecture notes in mathematics","volume":"940","author":"Shelah","year":"1982"},{"key":"S0022481200009154_ref008","doi-asserted-by":"publisher","DOI":"10.1007\/BF02780398"},{"key":"S0022481200009154_ref005","doi-asserted-by":"publisher","DOI":"10.4064\/fm-142-3-257-261"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200009154","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,7]],"date-time":"2019-05-07T00:18:21Z","timestamp":1557188301000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200009154\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,12]]},"references-count":9,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2002,12]]}},"alternative-id":["S0022481200009154"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1190150293","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,12]]}}}