{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,30]],"date-time":"2025-12-30T23:13:46Z","timestamp":1767136426404,"version":"build-2238731810"},"reference-count":6,"publisher":"Wiley","issue":"2","license":[{"start":{"date-parts":[[2024,7,6]],"date-time":"2024-07-06T00:00:00Z","timestamp":1720224000000},"content-version":"vor","delay-in-days":66,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003977","name":"Israel Science Foundation","doi-asserted-by":"publisher","award":["1838\/19"],"award-info":[{"award-number":["1838\/19"]}],"id":[{"id":"10.13039\/501100003977","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["DMS\u00a01833363"],"award-info":[{"award-number":["DMS\u00a01833363"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2024,5]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>The Ramsey Choice principle for families of \u2010element sets, denoted , states that every infinite set  has an infinite subset  with a choice function on . We investigate for which positive integers  and  the implication  is provable in\u00a0. It will turn out that beside the trivial implications , under the assumption that every odd integer  is the sum of three primes (known as ternary Goldbach conjecture), the only non\u2010trivial implication which is provable in  is .<\/jats:p>","DOI":"10.1002\/malq.202300024","type":"journal-article","created":{"date-parts":[[2024,7,7]],"date-time":"2024-07-07T00:08:00Z","timestamp":1720310880000},"page":"255-261","update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Implications of Ramsey Choice principles in ZF$\\mathsf {ZF}$"],"prefix":"10.1002","volume":"70","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6078-7237","authenticated-orcid":false,"given":"Lorenz","family":"Halbeisen","sequence":"first","affiliation":[{"name":"Department of Mathematics ETH Zentrum Zurich Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Riccardo","family":"Plati","sequence":"additional","affiliation":[{"name":"Department of Mathematics ETH Zentrum Zurich Switzerland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Saharon","family":"Shelah","sequence":"additional","affiliation":[{"name":"Einstein Institute of Mathematics The Hebrew University of Jerusalem Yerushalayim Israel"},{"name":"Department of Mathematics Hill Center \u2013 Busch Campus Rutgers, State University of New Jersey Highland Park USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2024,7,6]]},"reference":[{"key":"e_1_2_6_2_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-60231-8"},{"key":"e_1_2_6_3_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-022-00860-4"},{"key":"e_1_2_6_4_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00153-019-00705-7"},{"key":"e_1_2_6_5_1","unstructured":"H. A.Helfgott The ternary Goldbach conjecture is true Ann. Math. (to appear)."},{"key":"e_1_2_6_6_1","series-title":"Lecture Notes in Pure and Applied Mathematics","first-page":"57","volume-title":"Models, Algebras, and Proofs. Selected papers of the Xth Latin American Symposium on Mathematical Logic, held in Bogot\u00e1, Colombia, June 24\u201329, 1995","author":"Montenegro C. H.","year":"1998"},{"key":"e_1_2_6_7_1","doi-asserted-by":"publisher","DOI":"10.2307\/2272420"}],"updated-by":[{"DOI":"10.1002\/malq.202430002","type":"erratum","label":"Erratum","source":"publisher","updated":{"date-parts":[[2024,9,9]],"date-time":"2024-09-09T00:00:00Z","timestamp":1725840000000}}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.202300024","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,7,23]],"date-time":"2024-07-23T17:15:46Z","timestamp":1721754946000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.202300024"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,5]]},"references-count":6,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2024,5]]}},"alternative-id":["10.1002\/malq.202300024"],"URL":"https:\/\/doi.org\/10.1002\/malq.202300024","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,5]]},"assertion":[{"value":"2023-06-02","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-06-07","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-07-06","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}