{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T22:51:00Z","timestamp":1780527060006,"version":"3.54.1"},"reference-count":28,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2017,12]]},"abstract":"<jats:p> The resurrection axioms are forcing axioms introduced recently by Hamkins and Johnstone, developing on ideas of Chalons and Veli\u010dkovi\u0107. We introduce a stronger form of resurrection axioms (the iterated resurrection axioms [Formula: see text] for a class of forcings [Formula: see text] and a given ordinal [Formula: see text]), and show that [Formula: see text] implies generic absoluteness for the first-order theory of [Formula: see text] with respect to forcings in [Formula: see text] preserving the axiom, where [Formula: see text] is a cardinal which depends on [Formula: see text] ([Formula: see text] if [Formula: see text] is any among the classes of countably closed, proper, semiproper, stationary set preserving forcings). <\/jats:p><jats:p> We also prove that the consistency strength of these axioms is below that of a Mahlo cardinal for most forcing classes, and below that of a stationary limit of supercompact cardinals for the class of stationary set preserving posets. Moreover, we outline that simultaneous generic absoluteness for [Formula: see text] with respect to [Formula: see text] and for [Formula: see text] with respect to [Formula: see text] with [Formula: see text] is in principle possible, and we present several natural models of the Morse\u2013Kelley set theory where this phenomenon occurs (even for all [Formula: see text] simultaneously). Finally, we compare the iterated resurrection axioms (and the generic absoluteness results we can draw from them) with a variety of other forcing axioms, and also with the generic absoluteness results by Woodin and the second author. <\/jats:p>","DOI":"10.1142\/s0219061317500052","type":"journal-article","created":{"date-parts":[[2017,4,19]],"date-time":"2017-04-19T09:32:18Z","timestamp":1492594338000},"page":"1750005","source":"Crossref","is-referenced-by-count":7,"title":["Absoluteness via resurrection"],"prefix":"10.1142","volume":"17","author":[{"given":"Giorgio","family":"Audrito","sequence":"first","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e0 degli studi di Torino, Torino 10123, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Matteo","family":"Viale","sequence":"additional","affiliation":[{"name":"Dipartimento di Matematica, Universit\u00e0 degli studi di Torino, Torino 10123, Italy"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"219","published-online":{"date-parts":[[2017,11,27]]},"reference":[{"key":"S0219061317500052BIB003","doi-asserted-by":"publisher","DOI":"10.1007\/s001530050154"},{"key":"S0219061317500052BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-003-0210-2"},{"key":"S0219061317500052BIB005","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1096901764"},{"key":"S0219061317500052BIB006","doi-asserted-by":"publisher","DOI":"10.4064\/fm194-2-1"},{"key":"S0219061317500052BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-009-0121-y"},{"key":"S0219061317500052BIB008","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511758867.002"},{"key":"S0219061317500052BIB009","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0098398"},{"key":"S0219061317500052BIB010","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-014-0369-8"},{"key":"S0219061317500052BIB011","doi-asserted-by":"publisher","DOI":"10.1007\/s40879-015-0092-y"},{"key":"S0219061317500052BIB013","doi-asserted-by":"publisher","DOI":"10.1016\/S0168-0072(99)00010-X"},{"key":"S0219061317500052BIB014","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-014-0374-y"},{"key":"S0219061317500052BIB015","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2016.4"},{"key":"S0219061317500052BIB017","series-title":"Springer Monographs in Mathematics","volume-title":"Set Theory","author":"Jech T.","year":"2003"},{"key":"S0219061317500052BIB018","series-title":"Springer Monographs in Mathematics","volume-title":"The Higher Infinite","author":"Kanamori A.","year":"2003","edition":"2"},{"key":"S0219061317500052BIB019","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4190-4"},{"key":"S0219061317500052BIB020","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-014-0406-7"},{"key":"S0219061317500052BIB021","doi-asserted-by":"publisher","DOI":"10.1142\/S0219061315500051"},{"key":"S0219061317500052BIB022","series-title":"Studies in Logic (London)","volume-title":"Set Theory","volume":"34","author":"Kunen K.","year":"2011"},{"key":"S0219061317500052BIB023","doi-asserted-by":"publisher","DOI":"10.1090\/ulect\/032"},{"key":"S0219061317500052BIB024","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(75)90009-1"},{"key":"S0219061317500052BIB025","doi-asserted-by":"publisher","DOI":"10.1215\/00294527-2420666"},{"key":"S0219061317500052BIB026","first-page":"281","volume":"39","author":"Neeman I.","year":"1998","journal-title":"Comment. 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