{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,29]],"date-time":"2025-09-29T12:05:19Z","timestamp":1759147519019},"reference-count":6,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2021,1,17]],"date-time":"2021-01-17T00:00:00Z","timestamp":1610841600000},"content-version":"vor","delay-in-days":47,"URL":"http:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2020,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In the context of reverse mathematics, effective transfinite recursion refers to a principle that allows us to construct sequences of sets by recursion along arbitrary well orders, provided that each set is \u2010definable relative to the previous stages of the recursion. It is known that this principle is provable in\u00a0. In the present note, we argue that a common formulation of effective transfinite recursion is too restrictive. We then propose a more liberal formulation, which appears very natural and is still provable in\u00a0.<\/jats:p>","DOI":"10.1002\/malq.202000042","type":"journal-article","created":{"date-parts":[[2021,1,18]],"date-time":"2021-01-18T06:25:45Z","timestamp":1610951145000},"page":"479-483","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["What is effective transfinite recursion in reverse mathematics?"],"prefix":"10.1002","volume":"66","author":[{"given":"Anton","family":"Freund","sequence":"first","affiliation":[{"name":"Fachbereich Mathematik Technische Universit\u00e4t Darmstadt Schlossgartenstr. 7, 64289 Darmstadt Germany"}]}],"member":"311","published-online":{"date-parts":[[2021,1,17]]},"reference":[{"key":"e_1_2_3_2_1","unstructured":"D.Dzhafarov S.Flood R.Solomon andL. B.Westrick Effectiveness for the dual Ramsey theorem preprint (2017) arXiv:1710.00070."},{"key":"e_1_2_3_3_1","unstructured":"A.Freund Well ordering principles and\u03a041\u2010statements: a pilot study preprint (2020) arXiv:2006.12111."},{"key":"e_1_2_3_4_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-07-04285-7"},{"key":"e_1_2_3_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-12013-2"},{"key":"e_1_2_3_6_1","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511581007"},{"key":"e_1_2_3_7_1","doi-asserted-by":"publisher","DOI":"10.1016\/0168-0072(95)00029-G"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.202000042","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/full-xml\/10.1002\/malq.202000042","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.202000042","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,3]],"date-time":"2023-09-03T16:32:57Z","timestamp":1693758777000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.202000042"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,12]]},"references-count":6,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,12]]}},"alternative-id":["10.1002\/malq.202000042"],"URL":"https:\/\/doi.org\/10.1002\/malq.202000042","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,12]]},"assertion":[{"value":"2020-06-16","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2020-10-14","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-01-17","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}