{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,28]],"date-time":"2025-11-28T07:18:27Z","timestamp":1764314307461,"version":"3.46.0"},"reference-count":11,"publisher":"World Scientific Pub Co Pte Ltd","issue":"03","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:p>We prove that the forcing axiom [Formula: see text] implies [Formula: see text]. Using this implication, we show that the forcing axiom [Formula: see text] is inconsistent. We also derive weak Chang\u2019s Conjecture from [Formula: see text] and use this second implication to give another proof of the inconsistency of [Formula: see text].<\/jats:p>","DOI":"10.1142\/s0219061324500211","type":"journal-article","created":{"date-parts":[[2024,6,27]],"date-time":"2024-06-27T05:06:52Z","timestamp":1719464812000},"source":"Crossref","is-referenced-by-count":0,"title":["Consistent and inconsistent generalizations of Martin\u2019s Axiom, weak square and weak Chang\u2019s Conjecture"],"prefix":"10.1142","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7972-2860","authenticated-orcid":false,"given":"David","family":"Asper\u00f3","sequence":"first","affiliation":[{"name":"School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK"}]},{"given":"Nutt","family":"Tananimit","sequence":"additional","affiliation":[{"name":"School of Mathematics, University of East Anglia, Norwich NR4 7TJ, UK"}]}],"member":"219","published-online":{"date-parts":[[2024,6,26]]},"reference":[{"doi-asserted-by":"publisher","key":"S0219061324500211BIB001","DOI":"10.1016\/j.apal.2007.02.002"},{"doi-asserted-by":"publisher","key":"S0219061324500211BIB002","DOI":"10.1007\/s11856-015-1250-0"},{"doi-asserted-by":"publisher","key":"S0219061324500211BIB004","DOI":"10.1016\/0168-0072(89)90030-4"},{"doi-asserted-by":"publisher","key":"S0219061324500211BIB005","DOI":"10.2307\/1971415"},{"volume-title":"Set Theory: The Third Millenium Edition, Revised and Expanded","year":"2002","author":"Jech T.","key":"S0219061324500211BIB006"},{"volume-title":"Set Theory, An Introduction to Independence Proofs","year":"1980","author":"Kunen K.","key":"S0219061324500211BIB007"},{"doi-asserted-by":"publisher","key":"S0219061324500211BIB008","DOI":"10.1007\/s00153-017-0550-y"},{"doi-asserted-by":"publisher","key":"S0219061324500211BIB009","DOI":"10.4064\/fm215-2-2"},{"doi-asserted-by":"publisher","key":"S0219061324500211BIB010","DOI":"10.1007\/978-3-662-12831-2"},{"doi-asserted-by":"publisher","key":"S0219061324500211BIB011","DOI":"10.1007\/s00153-003-0208-9"},{"doi-asserted-by":"publisher","key":"S0219061324500211BIB012","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\/S0219061324500211","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,28]],"date-time":"2025-11-28T07:14:39Z","timestamp":1764314079000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219061324500211"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,6,26]]},"references-count":11,"journal-issue":{"issue":"03","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["10.1142\/S0219061324500211"],"URL":"https:\/\/doi.org\/10.1142\/s0219061324500211","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"type":"print","value":"0219-0613"},{"type":"electronic","value":"1793-6691"}],"subject":[],"published":{"date-parts":[[2024,6,26]]},"article-number":"2450021"}}