{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,28]],"date-time":"2023-09-28T05:40:17Z","timestamp":1695879617004},"reference-count":5,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":5430,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1992,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We introduce a class of forcing notions, called forcing notions of type <jats:italic>S<\/jats:italic>, which contains among other Sacks forcing, Prikry\u2010Silver forcing and their iterations and products with countable supports. We construct and investigate some formalism suitable for this forcing notions, which allows all standard tricks for iterations or products with countable supports of Sacks forcing. On the other hand it does not involve internal combinatorial structure of conditions of iterations or products. We prove that the class of forcing notions of type <jats:italic>S<\/jats:italic> is closed under products and certain iterations with countable supports.<\/jats:p>","DOI":"10.1002\/malq.19920380140","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T05:49:10Z","timestamp":1180417750000},"page":"413-421","source":"Crossref","is-referenced-by-count":1,"title":["A FORMALISM FOR SOME CLASS OF FORCING NOTIONS"],"prefix":"10.1002","volume":"38","author":[{"given":"Piotr","family":"Koszmider","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"P.","family":"Koszmider","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","series-title":"London Math. Soc. Lecture Notes Series 87","volume-title":"Iterated forcing","author":"Baumgartner J. E.","year":"1983"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0166-8641(85)90002-1"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01190417"},{"key":"e_1_2_1_5_2","unstructured":"Koszmider P. O uog\u00f3lnieniu forsingu Saksa z zastosowaniem w teorii algebr Boolea. Master Thesis (in Polish) Uniwersytet Warszawski 1987."},{"key":"e_1_2_1_6_2","volume-title":"Set Theory: Introduction to Independence Proofs","author":"Kunen K.","year":"1980"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19920380140","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19920380140","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T20:34:16Z","timestamp":1695846856000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19920380140"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,1]]},"references-count":5,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1992,1]]}},"alternative-id":["10.1002\/malq.19920380140"],"URL":"https:\/\/doi.org\/10.1002\/malq.19920380140","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,1]]}}}