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{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,9,15]],"date-time":"2023-09-15T01:49:01Z","timestamp":1694742541972},"reference-count":31,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2018,5,1]],"date-time":"2018-05-01T00:00:00Z","timestamp":1525132800000},"content-version":"unspecified","delay-in-days":61,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2018,3]]},"abstract":"Abstract<\/jats:title>I analyze the hierarchies of the bounded resurrection axioms and their \u201cvirtual\u201d versions, the virtual bounded resurrection axioms, for several classes of forcings (the emphasis being on the subcomplete forcings). I analyze these axioms in terms of implications and consistency strengths. For the virtual hierarchies, I provide level-by-level equiconsistencies with an appropriate hierarchy of virtual partially super-extendible cardinals. I show that the boldface resurrection axioms for subcomplete or countably closed forcing imply the failure of Todor\u010devi\u0107\u2019s square at the appropriate level. I also establish connections between these hierarchies and the hierarchies of bounded and weak bounded forcing axioms.<\/jats:p>","DOI":"10.1017\/jsl.2017.65","type":"journal-article","created":{"date-parts":[[2018,5,1]],"date-time":"2018-05-01T08:04:44Z","timestamp":1525161884000},"page":"283-325","source":"Crossref","is-referenced-by-count":2,"title":["HIERARCHIES OF (VIRTUAL) RESURRECTION AXIOMS"],"prefix":"10.1017","volume":"83","author":[{"given":"GUNTER","family":"FUCHS","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2018,5,1]]},"reference":[{"key":"S0022481217000652_ref8","article-title":"The subcompleteness of Magidor forcing","author":"Fuchs","year":"2017","journal-title":"Archive for Mathematical Logic"},{"key":"S0022481217000652_ref12","unstructured":"[12] Goldstern M. and Shelah S. , The bounded proper forcing axiom, this Journal, vol. 60 (1995), no. 1, pp. 58\u201373."},{"key":"S0022481217000652_ref17","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(72)90001-0"},{"key":"S0022481217000652_ref31","volume-title":"Subtle and ineffable tree properties","author":"Wei\u00df","year":"2010"},{"key":"S0022481217000652_ref27","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-5764-9_4"},{"key":"S0022481217000652_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/s001530050154"},{"key":"S0022481217000652_ref21","volume-title":"Set Theory. 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D. , A simple maximality principle, this Journal, vol. 68 (2003), no. 2, pp. 527\u2013550."},{"key":"S0022481217000652_ref1","doi-asserted-by":"publisher","DOI":"10.1002\/malq.200410015"},{"key":"S0022481217000652_ref4","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-2011-10730-5"},{"key":"S0022481217000652_ref6","unstructured":"[6] Fuchs G. , Closed maximality principles: Implications, separations and combinations, this Journal, vol. 73 (2008), no. 1, pp. 276\u2013308."},{"key":"S0022481217000652_ref7","unstructured":"[7] Fuchs G. , Combined maximality principles up to large cardinals, this Journal, vol. 74 (2009), no. 3, pp. 1015\u20131046."},{"key":"S0022481217000652_ref9","unstructured":"[9] Fuchs G. , Hierarchies of forcing axioms, the continuum hypothesis and square principles, this Journal, vol. 83 (2018), no. 1, pp. 256\u2013282."},{"key":"S0022481217000652_ref10","unstructured":"[10] Gitman V. , Ramsey-like cardinals, this Journal, vol. 76 (2011), no. 2, pp. 519\u2013540."},{"key":"S0022481217000652_ref11","unstructured":"[11] Gitman V. and Welch P. , Ramsey-like cardinals II, this Journal, vol. 76 (2011), no. 2, pp. 541\u2013560."},{"key":"S0022481217000652_ref14","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-014-0374-y"},{"key":"S0022481217000652_ref16","doi-asserted-by":"crossref","unstructured":"[16] Hayut Y. and Lambie-Hanson C. , Simultaneous stationary reflection and square sequences. Preprint, 2016, arXiv:1603.05556.","DOI":"10.1142\/S0219061317500106"},{"key":"S0022481217000652_ref18","unstructured":"[18] Jensen R. B. , Forcing axioms compatible with CH, handwritten notes, 2009. Available at: https:\/\/www.mathematik.hu-berlin.de\/\u223craesch\/org\/jensen.html."},{"key":"S0022481217000652_ref19","unstructured":"[19] Jensen R. B. , Subproper and subcomplete forcing, handwritten notes, 2009. Available at: https:\/\/www.mathematik.hu-berlin.de\/\u223craesch\/org\/jensen.html."},{"key":"S0022481217000652_ref20","doi-asserted-by":"publisher","DOI":"10.1142\/9789814602648_0002"},{"key":"S0022481217000652_ref23","first-page":"301","volume-title":"Appalachian Set Theory 2006\u20132012","volume":"406","author":"Magidor","year":"2013"},{"key":"S0022481217000652_ref24","unstructured":"[24] Moore J. T. , Set mapping reflection, this Journal, vol. 5 (2005), no. 1, pp. 87\u201397."},{"key":"S0022481217000652_ref26","volume-title":"Logic and Algebra","volume":"302","author":"Stavi","year":"2001"},{"key":"S0022481217000652_ref29","unstructured":"[29] Viale M. , Audrito G. , and Steila S. , A boolean algebraic approach to semiproper iterations. Preprint, 2014, arXiv:1402.1714 [math.LO]."}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481217000652","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,10,17]],"date-time":"2019-10-17T08:17:06Z","timestamp":1571300226000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481217000652\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,3]]},"references-count":31,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2018,3]]}},"alternative-id":["S0022481217000652"],"URL":"https:\/\/doi.org\/10.1017\/jsl.2017.65","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2018,3]]}}}