{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,13]],"date-time":"2025-02-13T05:07:49Z","timestamp":1739423269751,"version":"3.37.0"},"reference-count":5,"publisher":"Springer Science and Business Media LLC","issue":"1-2","license":[{"start":{"date-parts":[[2024,8,16]],"date-time":"2024-08-16T00:00:00Z","timestamp":1723766400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2024,8,16]],"date-time":"2024-08-16T00:00:00Z","timestamp":1723766400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100002869","name":"Christian-Albrechts-Universit\u00e4t zu Kiel","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100002869","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":[[2025,2]]},"abstract":"Abstract<\/jats:title>\n We investigate the covering numbers of some ideals on \n \n $${^{\\omega }}{2}{}$$<\/jats:tex-math>\n \n \n \n \n \n \u03c9<\/mml:mi>\n <\/mml:mmultiscripts>\n 2<\/mml:mn>\n \n <\/mml:mrow>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula> associated with tree forcings. We prove that the covering of the Sacks ideal remains small in the Silver and uniform Sacks model, respectively, and that the coverings of the uniform Sacks ideal and the Mycielski ideal, \n \n $${\\mathfrak {C}_{2}}$$<\/jats:tex-math>\n \n \n C<\/mml:mi>\n 2<\/mml:mn>\n <\/mml:msub>\n <\/mml:math>\n <\/jats:alternatives>\n <\/jats:inline-formula>, remain small in the Sacks model.<\/jats:p>","DOI":"10.1007\/s00153-024-00933-6","type":"journal-article","created":{"date-parts":[[2024,8,16]],"date-time":"2024-08-16T05:02:17Z","timestamp":1723784537000},"page":"259-278","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Different covering numbers of compact tree ideals"],"prefix":"10.1007","volume":"64","author":[{"given":"Jelle Mathis","family":"Kuiper","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Otmar","family":"Spinas","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2024,8,16]]},"reference":[{"key":"933_CR1","unstructured":"Brendle, J.: Combinatorial aspects of the meager and null ideals and other ideals on the reals, Eberhard-Karls-Universit\u00e4t T\u00fcbingen. unpublished habilitation thesis"},{"issue":"2","key":"933_CR2","doi-asserted-by":"publisher","first-page":"103","DOI":"10.4064\/fm282-7-2023","volume":"264","author":"JM Kuiper","year":"2024","unstructured":"Kuiper, J.M., Spinas, O.: Mycielski ideals and uniform trees. Fund. Math. 264(2), 103\u2013147 (2024). https:\/\/doi.org\/10.4064\/fm282-7-2023","journal-title":"Fund. Math."},{"issue":"1","key":"933_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.4064\/fm-148-1-1-25","volume":"148","author":"J Brendle","year":"1994","unstructured":"Brendle, J.: Strolling through paradise. Fund. Math. 148(1), 1\u201325 (1994)","journal-title":"Fund. Math."},{"issue":"3","key":"933_CR4","doi-asserted-by":"publisher","first-page":"145","DOI":"10.1007\/BF01269943","volume":"31","author":"H Judah","year":"1992","unstructured":"Judah, H., Miller, A.W., Shelah, S.: Sacks forcing, Laver forcing, and Martin\u2019s axiom. Arch. Math. Logic 31(3), 145\u2013161 (1992). https:\/\/doi.org\/10.1007\/BF01269943","journal-title":"Arch. Math. Logic"},{"key":"933_CR5","unstructured":"Spinas, O.: The covering numbers of some mycielski ideals may be different. preprint. https:\/\/www.math.uni-kiel.de\/logik\/de\/spinas\/forschung\/The%20covering%20numbers%20of%20some%20Mycielski%20ideals%20may%20be%20different.pdf"}],"container-title":["Archive for Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-024-00933-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00153-024-00933-6\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-024-00933-6.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,12]],"date-time":"2025-02-12T05:40:35Z","timestamp":1739338835000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00153-024-00933-6"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,16]]},"references-count":5,"journal-issue":{"issue":"1-2","published-print":{"date-parts":[[2025,2]]}},"alternative-id":["933"],"URL":"https:\/\/doi.org\/10.1007\/s00153-024-00933-6","relation":{},"ISSN":["0933-5846","1432-0665"],"issn-type":[{"type":"print","value":"0933-5846"},{"type":"electronic","value":"1432-0665"}],"subject":[],"published":{"date-parts":[[2024,8,16]]},"assertion":[{"value":"23 November 2023","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 May 2024","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"16 August 2024","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}