{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T11:20:25Z","timestamp":1769167225613,"version":"3.49.0"},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":4394,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2002,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>After presenting a general setting in which to look at forcing axioms, we give a hierarchy of generalized bounded forcing axioms that correspond level by level, in consistency strength, with the members of a natural hierarchy of large cardinals below a Mahlo. We give a general construction of models of generalized bounded forcing axioms. Then we consider the bounded forcing axiom for a class of partially ordered sets \u0393<jats:sub>1<\/jats:sub> such that, letting \u0393<jats:sub>0<\/jats:sub> be the class of all stationary-set-preserving partially ordered sets, one can prove the following:<\/jats:p><jats:p>(a) \u0393<jats:sub>0<\/jats:sub> \u2286 \u0393<jats:sub>1<\/jats:sub>,<\/jats:p><jats:p>(b) \u0393<jats:sub>0<\/jats:sub> = \u0393<jats:sub>1<\/jats:sub> if and only if <jats:italic>NS<\/jats:italic>\u03c9<jats:sub>1<\/jats:sub> is \u2135<jats:sub>1<\/jats:sub>-dense.<\/jats:p><jats:p>(c) If <jats:italic>P<\/jats:italic> \u2209 \u0393<jats:sub>1<\/jats:sub>, then <jats:italic>BFA<\/jats:italic>({<jats:italic>P<\/jats:italic>}) fails.<\/jats:p><jats:p>We call the bounded forcing axiom for \u0393<jats:sub>1<\/jats:sub><jats:italic>Maximal Bounded Forcing Axiom<\/jats:italic> (<jats:italic>MBFA<\/jats:italic>). Finally we prove <jats:italic>MBFA<\/jats:italic> consistent relative to the consistency of an inaccessible \u03a3<jats:sub>2<\/jats:sub>-correct cardinal which is a limit of strongly compact cardinals.<\/jats:p>","DOI":"10.2178\/jsl\/1190150034","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T14:12:10Z","timestamp":1197555130000},"page":"130-142","source":"Crossref","is-referenced-by-count":6,"title":["A maximal bounded forcing axiom"],"prefix":"10.1017","volume":"67","author":[{"given":"David","family":"Asper\u00f3","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200009890_ref012","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/031\/763902"},{"key":"S0022481200009890_ref013","unstructured":"Todor\u010devi\u0107 S. , Localized reflection and fragments of PFA, 1999, seminar notes."},{"key":"S0022481200009890_ref010","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12831-2"},{"key":"S0022481200009890_ref001","unstructured":"Asper\u00f3 D. , Bounded forcing axioms and the continuum, Ph.D. thesis, U. Barcelona, 2000."},{"key":"S0022481200009890_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-21723-8"},{"key":"S0022481200009890_ref003","unstructured":"Bagaria J. and Friedman S. , Generic absoluteness, to appear in Annals of Pure and Applied Logic."},{"key":"S0022481200009890_ref006","doi-asserted-by":"publisher","DOI":"10.2307\/1971415"},{"key":"S0022481200009890_ref007","first-page":"58","volume":"60","author":"Goldstern","year":"1995","journal-title":"The bounded proper forcing axiom"},{"key":"S0022481200009890_ref008","volume-title":"Set theory. An introduction to independence proofs","author":"Kunen","year":"1980"},{"key":"S0022481200009890_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/s001530050154"},{"key":"S0022481200009890_ref014","doi-asserted-by":"publisher","DOI":"10.1515\/9783110804737"},{"key":"S0022481200009890_ref004","first-page":"481","volume":"41","author":"Baumgartner","year":"1976","journal-title":"Adding a closed unbounded set"},{"key":"S0022481200009890_ref009","unstructured":"Miyamoto T. , Localized reflecting cardinals and weak segments of PFA, preprint."},{"key":"S0022481200009890_ref011","unstructured":"Stavi J. and V\u00e4\u00e4n\u00e4nen J. , Reflection principles for the continuum, preprint."}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200009890","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,6]],"date-time":"2019-05-06T21:33:59Z","timestamp":1557178439000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200009890\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,3]]},"references-count":14,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2002,3]]}},"alternative-id":["S0022481200009890"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1190150034","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,3]]}}}