{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,15]],"date-time":"2024-09-15T22:32:32Z","timestamp":1726439552207},"reference-count":7,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2015,12]]},"abstract":"<jats:p> We develop a general framework for forcing with coherent adequate sets on [Formula: see text] as side conditions, where [Formula: see text] is a cardinal of uncountable cofinality. We describe a class of forcing posets which we call coherent adequate type forcings. The main theorem of the paper is that any coherent adequate type forcing preserves CH. We show that there exists a forcing poset for adding a club subset of [Formula: see text] with finite conditions while preserving CH, solving a problem of Friedman [Forcing with finite conditions, in Set Theory: Centre de Recerca Matem\u00e1tica, Barcelona, 2003\u20132004, Trends in Mathematics (Birkh\u00e4user-Verlag, 2006), pp. 285\u2013295.]. <\/jats:p>","DOI":"10.1142\/s0219061315500051","type":"journal-article","created":{"date-parts":[[2015,8,21]],"date-time":"2015-08-21T07:04:27Z","timestamp":1440140667000},"page":"1550005","source":"Crossref","is-referenced-by-count":6,"title":["Coherent adequate forcing and preserving CH"],"prefix":"10.1142","volume":"15","author":[{"given":"John","family":"Krueger","sequence":"first","affiliation":[{"name":"Department of Mathematics, University of North Texas, 1155 Union Circle #311430, Denton, TX 76203, USA"}]},{"given":"Miguel Angel","family":"Mota","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1ticas, Instituto Tecnol\u00f3gico Aut\u00f3nomo de M\u00e9xico, 01080 Ciudad de M\u00e9xico, D.F., Mexico"}]}],"member":"219","published-online":{"date-parts":[[2016,1,13]]},"reference":[{"key":"S0219061315500051BIB001","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-2015-06205-9"},{"key":"S0219061315500051BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/3-7643-7692-9_10"},{"key":"S0219061315500051BIB004","doi-asserted-by":"publisher","DOI":"10.4064\/fm224-3-5"},{"key":"S0219061315500051BIB005","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-014-0406-7"},{"key":"S0219061315500051BIB007","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-08-04664-3"},{"key":"S0219061315500051BIB009","doi-asserted-by":"publisher","DOI":"10.1215\/00294527-2420666"},{"key":"S0219061315500051BIB010","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/031\/763902"}],"container-title":["Journal of Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219061315500051","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T22:49:22Z","timestamp":1565131762000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219061315500051"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12]]},"references-count":7,"journal-issue":{"issue":"02","published-online":{"date-parts":[[2016,1,13]]},"published-print":{"date-parts":[[2015,12]]}},"alternative-id":["10.1142\/S0219061315500051"],"URL":"https:\/\/doi.org\/10.1142\/s0219061315500051","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"type":"print","value":"0219-0613"},{"type":"electronic","value":"1793-6691"}],"subject":[],"published":{"date-parts":[[2015,12]]}}}