{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,6]],"date-time":"2026-03-06T08:11:27Z","timestamp":1772784687402,"version":"3.50.1"},"reference-count":24,"publisher":"World Scientific Pub Co Pte Lt","issue":"01","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2005,6]]},"abstract":"<jats:p> In this note we will discuss a new reflection principle which follows from the Proper Forcing Axiom. The immediate purpose will be to prove that the bounded form of the Proper Forcing Axiom implies both that 2<jats:sup>\u03c9<\/jats:sup> = \u03c9<jats:sub>2<\/jats:sub> and that [Formula: see text] satisfies the Axiom of Choice. It will also be demonstrated that this reflection principle implies that \u25a1(\u03ba) fails for all regular \u03ba &gt; \u03c9<jats:sub>1<\/jats:sub>. <\/jats:p>","DOI":"10.1142\/s0219061305000407","type":"journal-article","created":{"date-parts":[[2005,6,22]],"date-time":"2005-06-22T11:49:55Z","timestamp":1119440995000},"page":"87-97","source":"Crossref","is-referenced-by-count":43,"title":["SET MAPPING REFLECTION"],"prefix":"10.1142","volume":"05","author":[{"given":"JUSTIN TATCH","family":"MOORE","sequence":"first","affiliation":[{"name":"Department of Mathematics, Boise State University, Boise, Idaho 83725, USA"}]}],"member":"219","published-online":{"date-parts":[[2011,11,21]]},"reference":[{"key":"rf2","doi-asserted-by":"publisher","DOI":"10.1007\/s001530050154"},{"key":"rf3","volume-title":"Handbook of Set-Theoretic Topology","author":"Baumgartner J.","year":"1984"},{"key":"rf4","doi-asserted-by":"crossref","first-page":"101","DOI":"10.4064\/fm-79-2-101-106","volume":"79","author":"Baumgartner J. E.","journal-title":"Fund. Math."},{"key":"rf5","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0098398","volume-title":"Topics in Set Theory","author":"Bekkali M.","year":"1991"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511758867.003"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.2307\/1971415"},{"key":"rf8","doi-asserted-by":"publisher","DOI":"10.2307\/2275509"},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-22400-7"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(72)90001-0"},{"key":"rf11","series-title":"Studies in Logic and the Foundations of Mathematics","volume-title":"An Introduction to Independence Proofs","volume":"102","author":"Kunen K.","year":"1983"},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.2307\/2687750"},{"key":"rf14","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0096536"},{"key":"rf15","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12831-2"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.2307\/1970860"},{"key":"rf18","doi-asserted-by":"publisher","DOI":"10.2307\/1999642"},{"key":"rf19","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/031\/763902"},{"key":"rf20","doi-asserted-by":"publisher","DOI":"10.1007\/BF02392561"},{"key":"rf21","doi-asserted-by":"crossref","unstructured":"S.\u00a0Todorcevic, Logic Colloquium '86 (Hull, 1986), Studies in Logic and the Foundations of Mathematics\u00a0124 (North-Holland, Amsterdam, 1988)\u00a0pp. 325\u2013331.","DOI":"10.1016\/S0049-237X(09)70663-9"},{"key":"rf22","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/084"},{"key":"rf23","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-0487-8_8"},{"key":"rf24","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-017-0487-8_8"},{"key":"rf25","doi-asserted-by":"publisher","DOI":"10.4310\/MRL.2002.v9.n4.a6"},{"key":"rf26","doi-asserted-by":"publisher","DOI":"10.1016\/0001-8708(92)90038-M"},{"key":"rf27","doi-asserted-by":"publisher","DOI":"10.1515\/9783110804737"}],"container-title":["Journal of Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219061305000407","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,6]],"date-time":"2019-08-06T12:32:37Z","timestamp":1565094757000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219061305000407"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2005,6]]},"references-count":24,"journal-issue":{"issue":"01","published-online":{"date-parts":[[2011,11,21]]},"published-print":{"date-parts":[[2005,6]]}},"alternative-id":["10.1142\/S0219061305000407"],"URL":"https:\/\/doi.org\/10.1142\/s0219061305000407","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"value":"0219-0613","type":"print"},{"value":"1793-6691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2005,6]]}}}