{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,25]],"date-time":"2026-01-25T02:02:29Z","timestamp":1769306549059,"version":"3.49.0"},"reference-count":9,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2025,10,4]],"date-time":"2025-10-04T00:00:00Z","timestamp":1759536000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2025,10,4]],"date-time":"2025-10-04T00:00:00Z","timestamp":1759536000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100004375","name":"Tel Aviv University","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100004375","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":[[2026,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We use indecomposable ultrafilters to answer some questions from Hayut and Karagila (in Comments Math Univ Carolin 60(2):285\u2013298, 2019). It is shown that the bound on the strength of Usuba (in A note on uniform ultrafilters in choiceless context,\n                    <jats:ext-link xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xlink:href=\"http:\/\/arxiv.org\/abs\/2401.04871\" ext-link-type=\"uri\">arXiv:2401.04871v1<\/jats:ext-link>\n                    ) is optimal.\n                  <\/jats:p>","DOI":"10.1007\/s00153-025-00983-4","type":"journal-article","created":{"date-parts":[[2025,10,4]],"date-time":"2025-10-04T03:16:20Z","timestamp":1759547780000},"page":"99-108","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["On ultrafilters in ZF models and indecomposable ultrafilters"],"prefix":"10.1007","volume":"65","author":[{"given":"Eilon","family":"Bilinsky","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Moti","family":"Gitik","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,10,4]]},"reference":[{"key":"983_CR1","first-page":"1029","volume":"51","author":"S Ben David","year":"1986","unstructured":"Ben David, S., Magidor, M.: The weak $$\\square ^*$$ is really weaker than the full $$\\square$$. JSL 51, 1029\u20131033 (1986)","journal-title":"JSL"},{"issue":"3","key":"983_CR2","doi-asserted-by":"publisher","first-page":"289","DOI":"10.1007\/BF02778036","volume":"63","author":"D Donder","year":"1988","unstructured":"Donder, D.: Regularity of ultrafilters and the core model. Israel J. Math. 63(3), 289\u2013322 (1988)","journal-title":"Israel J. Math."},{"key":"983_CR3","unstructured":"Gitik, M.: On $$\\sigma$$-complete uniform ultrafilters, to appear"},{"issue":"2","key":"983_CR4","first-page":"285","volume":"60","author":"Y Hayut","year":"2019","unstructured":"Hayut, Y., Karagila, A.: Spectra of uniformity. Comments Math. Univ. Carolin. 60(2), 285\u2013298 (2019)","journal-title":"Comments Math. Univ. Carolin."},{"key":"983_CR5","unstructured":"Jech, T.: The axiom of choice. North-Holland (1973)"},{"key":"983_CR6","unstructured":"Prikry, K.: Changing measurable into accessible cardinals. Dissertations Mathematicae 68 (1970)"},{"issue":"4","key":"983_CR7","first-page":"1000","volume":"48","author":"M Sheard","year":"1984","unstructured":"Sheard, M.: Indecomposable ultrafilters over small large cardinals. JSL 48(4), 1000\u20131007 (1984)","journal-title":"JSL"},{"key":"983_CR8","doi-asserted-by":"crossref","unstructured":"Silver, J.: Indecomposable ultrafilters and $$o\\sharp$$. In Proceedings of the Tarski Symposium, Proceedings of Symposia in Pure Mathematics, vol. 25. American Mathematical Society, Providence, R.I., pp. 357\u2013364 (1974)","DOI":"10.1090\/pspum\/025\/0360276"},{"key":"983_CR9","unstructured":"Usuba, T.: A note on uniform ultrafilters in choiceless context. arXiv:2401.04871v1"}],"container-title":["Archive for Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-025-00983-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00153-025-00983-4","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-025-00983-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,1,23]],"date-time":"2026-01-23T23:02:56Z","timestamp":1769209376000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00153-025-00983-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,4]]},"references-count":9,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,1]]}},"alternative-id":["983"],"URL":"https:\/\/doi.org\/10.1007\/s00153-025-00983-4","relation":{},"ISSN":["0933-5846","1432-0665"],"issn-type":[{"value":"0933-5846","type":"print"},{"value":"1432-0665","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,10,4]]},"assertion":[{"value":"30 July 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 August 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"4 October 2025","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}]}}