{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T02:16:33Z","timestamp":1772504193569,"version":"3.50.1"},"reference-count":12,"publisher":"Wiley","issue":"6","license":[{"start":{"date-parts":[[2004,10,1]],"date-time":"2004-10-01T00:00:00Z","timestamp":1096588800000},"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":[[2004,10]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We show that <jats:italic>L<\/jats:italic>(\u211d) absoluteness for semi\u2010proper forcings is equiconsistent with the existence of a remarkable cardinal, and hence by [6] with <jats:italic>L<\/jats:italic>(\u211d) absoluteness for proper forcings. By [7], <jats:italic>L<\/jats:italic>(\u211d) absoluteness for stationary set preserving forcings gives an inner model with a strong cardinal. By [3], the Bounded Semi\u2010Proper Forcing Axiom (BSPFA) is equiconsistent with the Bounded Proper Forcing Axiom (BPFA), which in turn is equiconsistent with a reflecting cardinal. We show that Bounded Martin's Maximum (BMM) is much stronger than BSPFA in that if BMM holds, then for every <jats:italic>X<\/jats:italic> \u2208 <jats:italic>V<\/jats:italic> , <jats:italic>X<\/jats:italic><jats:sup>#<\/jats:sup> exists. (\u00a9 2004 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200410002","type":"journal-article","created":{"date-parts":[[2004,10,4]],"date-time":"2004-10-04T16:01:01Z","timestamp":1096905661000},"page":"527-532","source":"Crossref","is-referenced-by-count":11,"title":["Semi\u2010proper forcing, remarkable cardinals, and Bounded Martin's Maximum"],"prefix":"10.1002","volume":"50","author":[{"given":"Ralf","family":"Schindler","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2004,10]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1190150154"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.2307\/2275649"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.2307\/2275509"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.2307\/1970813"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.2307\/2695045"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.2307\/421205"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-00-02636-2"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.2307\/2695120"},{"key":"e_1_2_1_10_2","unstructured":"R.Schindler Bounded Martin's Maximum and strong cardinals. Preprint. (available at www.math.uni\u2010muenster.de\/math\/inst\/logik\/org\/staff\/rds."},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.2307\/2274385"},{"key":"e_1_2_1_12_2","doi-asserted-by":"crossref","unstructured":"S.Shelah andL.Stanley Coding and reshaping when there are no sharps. In: Set Theory of the Continuum (H. Judah et al. eds.) pp. 407\u2013416 (Springer\u2010Verlag New York et al. 1992).","DOI":"10.1007\/978-1-4613-9754-0_21"},{"key":"e_1_2_1_13_2","unstructured":"W. H.Woodin Private communication August 2003."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200410002","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200410002","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,18]],"date-time":"2023-10-18T21:00:45Z","timestamp":1697662845000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200410002"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,10]]},"references-count":12,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2004,10]]}},"alternative-id":["10.1002\/malq.200410002"],"URL":"https:\/\/doi.org\/10.1002\/malq.200410002","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,10]]}}}