{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,19]],"date-time":"2026-03-19T05:33:59Z","timestamp":1773898439489,"version":"3.50.1"},"reference-count":11,"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":[[2021,8]]},"abstract":"<jats:p> We establish natural criteria under which normally iterable premice are iterable for stacks of normal trees. Let [Formula: see text] be a regular uncountable cardinal. Let [Formula: see text] and [Formula: see text] be an [Formula: see text]-sound premouse and [Formula: see text] be an [Formula: see text]-iteration strategy for [Formula: see text] (roughly, a normal [Formula: see text]-strategy). We define a natural condensation property for iteration strategies, inflation condensation. We show that if [Formula: see text] has inflation condensation then [Formula: see text] is [Formula: see text]-iterable (roughly, [Formula: see text] is iterable for length [Formula: see text] stacks of normal trees each of length [Formula: see text]), and moreover, we define a specific such strategy [Formula: see text] and a reduction of stacks via [Formula: see text] to normal trees via [Formula: see text]. If [Formula: see text] has the Dodd-Jensen property and [Formula: see text] then [Formula: see text] has inflation condensation. We also apply some of the techniques developed to prove that if [Formula: see text] has strong hull condensation (introduced independently by John Steel), and [Formula: see text] is [Formula: see text]-generic for an [Formula: see text]-cc forcing, then [Formula: see text] extends to an [Formula: see text]-strategy [Formula: see text] for [Formula: see text] with strong hull condensation, in the sense of [Formula: see text]. Moreover, this extension is unique. We deduce that if [Formula: see text] is [Formula: see text]-generic for a ccc forcing then [Formula: see text] and [Formula: see text] have the same [Formula: see text]-sound, [Formula: see text]-iterable premice which project to [Formula: see text]. <\/jats:p>","DOI":"10.1142\/s0219061321500082","type":"journal-article","created":{"date-parts":[[2020,8,31]],"date-time":"2020-08-31T15:34:38Z","timestamp":1598888078000},"page":"2150008","source":"Crossref","is-referenced-by-count":5,"title":["Iterability for (transfinite) stacks"],"prefix":"10.1142","volume":"21","author":[{"given":"Farmer","family":"Schlutzenberg","sequence":"first","affiliation":[{"name":"Fachbereich Mathematik und Informatik, WWU M\u00fcnster, Einsteinstra\u00dfe 62, 48149 M\u00fcnster, Germany"}]}],"member":"219","published-online":{"date-parts":[[2021,4,26]]},"reference":[{"key":"S0219061321500082BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-21903-4"},{"key":"S0219061321500082BIB005","doi-asserted-by":"publisher","DOI":"10.2307\/2586630"},{"key":"S0219061321500082BIB006","series-title":"(1111) of Memoirs of the AMS","volume-title":"Hod Mice and the Mouse Set Conjecture","volume":"236","author":"Sargsyan G.","year":"2015"},{"key":"S0219061321500082BIB008","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(94)00036-3"},{"key":"S0219061321500082BIB009","doi-asserted-by":"publisher","DOI":"10.2307\/2275679"},{"key":"S0219061321500082BIB010","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1245158084"},{"key":"S0219061321500082BIB018","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2020.102826"},{"key":"S0219061321500082BIB022","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-22485-4"},{"key":"S0219061321500082BIB023","doi-asserted-by":"publisher","DOI":"10.2178\/jsl\/1190150159"},{"key":"S0219061321500082BIB024","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-5764-9_20"},{"key":"S0219061321500082BIB025","volume-title":"de Gruyter Series in Logic and its Applications","author":"Zeman M.","year":"2002"}],"container-title":["Journal of Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219061321500082","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,26]],"date-time":"2021-07-26T09:09:14Z","timestamp":1627290554000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0219061321500082"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,4,26]]},"references-count":11,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2021,8]]}},"alternative-id":["10.1142\/S0219061321500082"],"URL":"https:\/\/doi.org\/10.1142\/s0219061321500082","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"value":"0219-0613","type":"print"},{"value":"1793-6691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,4,26]]}}}