{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T12:08:01Z","timestamp":1759147681170},"reference-count":14,"publisher":"Wiley","issue":"1-2","license":[{"start":{"date-parts":[[2017,3,31]],"date-time":"2017-03-31T00:00:00Z","timestamp":1490918400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2017,4]]},"abstract":"<jats:p>We present a general framework for forcing on \u03c9<jats:sub>2<\/jats:sub> with finite conditions using countable models as side conditions. This framework is based on a method of comparing countable models as being membership related up to a large initial segment. We give several examples of this type of forcing, including adding a function on \u03c9<jats:sub>2<\/jats:sub>, adding a nonreflecting stationary subset of <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"graphic\/malq201400022-math-0001.png\" xlink:title=\"urn:x-wiley:09425616:media:malq201400022:malq201400022-math-0001\" \/>, and adding an \u03c9<jats:sub>1<\/jats:sub>\u2010Kurepa tree.<\/jats:p>","DOI":"10.1002\/malq.201400022","type":"journal-article","created":{"date-parts":[[2017,3,31]],"date-time":"2017-03-31T15:36:13Z","timestamp":1490974573000},"page":"124-149","source":"Crossref","is-referenced-by-count":3,"title":["Forcing with adequate sets of models as side conditions"],"prefix":"10.1002","volume":"63","author":[{"given":"John","family":"Krueger","sequence":"first","affiliation":[{"name":"Department of Mathematics University of North Texas 1155 Union Circle #311430 Denton TX 76203 United States of America"}]}],"member":"311","published-online":{"date-parts":[[2017,3,31]]},"reference":[{"key":"e_1_2_11_2_1","doi-asserted-by":"publisher","DOI":"10.2478\/s11533-012-0037-3"},{"key":"e_1_2_11_3_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2012.09.002"},{"key":"e_1_2_11_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/3-7643-7692-9_10"},{"key":"e_1_2_11_5_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-06-04163-8"},{"key":"e_1_2_11_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF02803525"},{"key":"e_1_2_11_7_1","doi-asserted-by":"publisher","DOI":"10.4064\/fm224-3-5"},{"key":"e_1_2_11_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-013-0358-3"},{"key":"e_1_2_11_9_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-014-0406-7"},{"key":"e_1_2_11_10_1","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061315500051"},{"key":"e_1_2_11_11_1","doi-asserted-by":"publisher","DOI":"10.1305\/ndjfl\/1125409334"},{"key":"e_1_2_11_12_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-08-04664-3"},{"key":"e_1_2_11_13_1","doi-asserted-by":"publisher","DOI":"10.1215\/00294527-2420666"},{"key":"e_1_2_11_14_1","first-page":"209","volume-title":"Axiomatic Set Theory, Proceedings of the American Mathematical Society Summer Research Conference on Axiomatic Set Theory, held in Boulder, Colorado, June 19\u201325 1983, Contemporary Mathematics Vol. 31","author":"Todor\u010devi\u0107 S.","year":"1984"},{"key":"e_1_2_11_15_1","first-page":"331","volume-title":"Appalachian Set Theory: 2006\u20132012, London Mathematical Society Lecture Notes Series Vol. 406","author":"Veli\u010dkovi\u0107 B.","year":"2013"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.201400022","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201400022","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/malq.201400022","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.201400022","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,4]],"date-time":"2023-09-04T03:58:56Z","timestamp":1693799936000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.201400022"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,3,31]]},"references-count":14,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2017,4]]}},"alternative-id":["10.1002\/malq.201400022"],"URL":"https:\/\/doi.org\/10.1002\/malq.201400022","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,3,31]]}}}