{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T03:23:11Z","timestamp":1740108191693,"version":"3.37.3"},"reference-count":4,"publisher":"Springer Science and Business Media LLC","issue":"3-4","license":[{"start":{"date-parts":[[2022,9,19]],"date-time":"2022-09-19T00:00:00Z","timestamp":1663545600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2022,9,19]],"date-time":"2022-09-19T00:00:00Z","timestamp":1663545600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100004869","name":"Westf\u00e4lische Wilhelms-Universit\u00e4t M\u00fcnster","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100004869","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Arch. Math. Logic"],"published-print":{"date-parts":[[2023,5]]},"abstract":"Abstract<\/jats:title>We show it is consistent that there is a Souslin tree S<\/jats:italic> such that after forcing with S<\/jats:italic>, S<\/jats:italic> is Kurepa and for all clubs $$C \\subset \\omega _1$$<\/jats:tex-math>\n \n C<\/mml:mi>\n \u2282<\/mml:mo>\n \n \u03c9<\/mml:mi>\n 1<\/mml:mn>\n <\/mml:msub>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>, $$S\\upharpoonright C$$<\/jats:tex-math>\n \n S<\/mml:mi>\n \u21be<\/mml:mo>\n C<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> is rigid. This answers the questions in Fuchs (Arch Math Logic 52(1\u20132):47\u201366, 2013). Moreover, we show it is consistent with $$\\diamondsuit $$<\/jats:tex-math>\n \u2662<\/mml:mo>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> that for every Souslin tree T<\/jats:italic> there is a dense $$X \\subseteq T$$<\/jats:tex-math>\n \n X<\/mml:mi>\n \u2286<\/mml:mo>\n T<\/mml:mi>\n <\/mml:mrow>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> which does not contain a copy of T<\/jats:italic>. This is related to a question due to Baumgartner in Baumgartner (Ordered sets (Banff, Alta., 1981), volume 83 of NATO Adv. Study Inst. Ser. C: Math. Phys. Sci., Reidel, Dordrecht-Boston, pp 239\u2013277, 1982).<\/jats:p>","DOI":"10.1007\/s00153-022-00843-5","type":"journal-article","created":{"date-parts":[[2022,9,19]],"date-time":"2022-09-19T18:08:36Z","timestamp":1663610916000},"page":"419-426","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On the rigidity of Souslin trees and their generic branches"],"prefix":"10.1007","volume":"62","author":[{"given":"Hossein","family":"Lamei Ramandi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,9,19]]},"reference":[{"key":"843_CR1","doi-asserted-by":"crossref","unstructured":"Baumgartner, J.E.: Order types of real numbers and other uncountable orderings. In: Ordered sets (Banff, Alta., 1981), volume 83 of NATO Adv. Study Inst. Ser. C: Math. Phys. Sci., pp 239\u2013277. Reidel, Dordrecht-Boston, Mass (1982)","DOI":"10.1007\/978-94-009-7798-3_7"},{"issue":"1\u20132","key":"843_CR2","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/s00153-012-0306-7","volume":"52","author":"G Fuchs","year":"2013","unstructured":"Fuchs, G.: Club degrees of rigidity and almost Kurepa trees. Arch. Math. Logic 52(1\u20132), 47\u201366 (2013)","journal-title":"Arch. Math. Logic"},{"issue":"2","key":"843_CR3","doi-asserted-by":"publisher","first-page":"423","DOI":"10.2178\/jsl\/1243948321","volume":"74","author":"G Fuchs","year":"2009","unstructured":"Fuchs, G., Hamkins, J.D.: Degrees of rigidity for Souslin trees. J. Symb. Logic 74(2), 423\u2013454 (2009)","journal-title":"J. Symb. Logic"},{"key":"843_CR4","unstructured":"Kunen, K.: An Introduction to Independence Proofs, volume 102 of Studies in Logic and the Foundations of Mathematics. North-Holland, Amsterdam (1983)"}],"container-title":["Archive for Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-022-00843-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00153-022-00843-5\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-022-00843-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,4,17]],"date-time":"2023-04-17T03:46:52Z","timestamp":1681703212000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00153-022-00843-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,9,19]]},"references-count":4,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2023,5]]}},"alternative-id":["843"],"URL":"https:\/\/doi.org\/10.1007\/s00153-022-00843-5","relation":{},"ISSN":["0933-5846","1432-0665"],"issn-type":[{"type":"print","value":"0933-5846"},{"type":"electronic","value":"1432-0665"}],"subject":[],"published":{"date-parts":[[2022,9,19]]},"assertion":[{"value":"13 October 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 August 2022","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"19 September 2022","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}