{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,3]],"date-time":"2026-03-03T08:28:18Z","timestamp":1772526498049,"version":"3.50.1"},"reference-count":15,"publisher":"World Scientific Pub Co Pte Ltd","issue":"02","funder":[{"name":"the European Union\u2019s Horizon 2020","award":["842082"],"award-info":[{"award-number":["842082"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Math. Log."],"published-print":{"date-parts":[[2022,8]]},"abstract":"<jats:p> Motivated by results of Bagaria, Magidor and V\u00e4\u00e4n\u00e4nen, we study characterizations of large cardinal properties through reflection principles for classes of structures. More specifically, we aim to characterize notions from the lower end of the large cardinal hierarchy through the principle\u00a0[Formula: see text]\u00a0introduced by Bagaria and V\u00e4\u00e4n\u00e4nen. Our results isolate a narrow interval in the large cardinal hierarchy that is bounded from below by total indescribability and from above by subtleness, and contains all large cardinals that can be characterized through the validity of the principle\u00a0[Formula: see text]\u00a0for all classes of structures defined by formulas in a fixed level of the L\u00e9vy hierarchy. Moreover, it turns out that no property that can be characterized through this principle can provably imply strong inaccessibility. The proofs of these results rely heavily on the notion of shrewd cardinals, introduced by Rathjen in a proof-theoretic context, and embedding characterizations of these cardinals that resembles Magidor\u2019s classical characterization of supercompactness. In addition, we show that several important weak large cardinal properties, like weak inaccessibility, weak Mahloness or weak\u00a0[Formula: see text]-indescribability, can be canonically characterized through localized versions of the principle\u00a0[Formula: see text]. Finally, the techniques developed in the proofs of these characterizations also allow us to show that Hamkin\u2019s weakly compact embedding property is equivalent to L\u00e9vy\u2019s notion of weak\u00a0[Formula: see text]-indescribability. <\/jats:p>","DOI":"10.1142\/s0219061322500076","type":"journal-article","created":{"date-parts":[[2022,2,7]],"date-time":"2022-02-07T08:05:10Z","timestamp":1644221110000},"source":"Crossref","is-referenced-by-count":5,"title":["Structural reflection, shrewd cardinals and the size of the continuum"],"prefix":"10.1142","volume":"22","author":[{"given":"Philipp","family":"L\u00fccke","sequence":"first","affiliation":[{"name":"Institut de Matem\u00e0tica, Universitat de Barcelona, Gran via de les Corts Catalanes 585, 08007 Barcelona, Spain"}]}],"member":"219","published-online":{"date-parts":[[2022,2,5]]},"reference":[{"key":"S0219061322500076BIB001","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-011-0261-8"},{"key":"S0219061322500076BIB003","doi-asserted-by":"publisher","DOI":"10.4171\/JEMS\/511"},{"key":"S0219061322500076BIB004","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-016-0511-x"},{"key":"S0219061322500076BIB005","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2015.60"},{"key":"S0219061322500076BIB007","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4020-5764-9_7"},{"key":"S0219061322500076BIB008","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-21723-8"},{"key":"S0219061322500076BIB010","doi-asserted-by":"publisher","DOI":"10.1016\/j.apal.2018.10.002"},{"key":"S0219061322500076BIB011","series-title":"Springer Monographs in Mathematics","volume-title":"Set Theory","author":"Jech T.","year":"2003"},{"key":"S0219061322500076BIB014","series-title":"Springer Monographs in Mathematics","volume-title":"The Higher Infinite: Large Cardinals in Set Theory from Their Beginnings","author":"Kanamori A.","year":"2003","edition":"2"},{"key":"S0219061322500076BIB015","doi-asserted-by":"publisher","DOI":"10.1090\/pspum\/013.1\/0281606"},{"key":"S0219061322500076BIB016","doi-asserted-by":"publisher","DOI":"10.1007\/BF02771565"},{"key":"S0219061322500076BIB017","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-004-0232-4"},{"key":"S0219061322500076BIB018","doi-asserted-by":"publisher","DOI":"10.2307\/2695120"},{"key":"S0219061322500076BIB019","doi-asserted-by":"publisher","DOI":"10.1016\/S0049-237X(08)71637-9"},{"key":"S0219061322500076BIB020","doi-asserted-by":"publisher","DOI":"10.1017\/jsl.2018.76"}],"container-title":["Journal of Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219061322500076","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,10,10]],"date-time":"2022-10-10T04:07:16Z","timestamp":1665374836000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0219061322500076"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,2,5]]},"references-count":15,"journal-issue":{"issue":"02","published-print":{"date-parts":[[2022,8,1]]}},"alternative-id":["10.1142\/S0219061322500076"],"URL":"https:\/\/doi.org\/10.1142\/s0219061322500076","relation":{},"ISSN":["0219-0613","1793-6691"],"issn-type":[{"value":"0219-0613","type":"print"},{"value":"1793-6691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,2,5]]},"article-number":"2250007"}}