{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T22:50:36Z","timestamp":1772491836298,"version":"3.50.1"},"reference-count":13,"publisher":"Springer Science and Business Media LLC","issue":"7-8","license":[{"start":{"date-parts":[[2025,3,15]],"date-time":"2025-03-15T00:00:00Z","timestamp":1741996800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,3,15]],"date-time":"2025-03-15T00:00:00Z","timestamp":1741996800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Arch. Math. Logic"],"published-print":{"date-parts":[[2025,11]]},"DOI":"10.1007\/s00153-025-00968-3","type":"journal-article","created":{"date-parts":[[2025,3,15]],"date-time":"2025-03-15T07:35:14Z","timestamp":1742024114000},"page":"917-933","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Reflection ranks via infinitary derivations"],"prefix":"10.1007","volume":"64","author":[{"given":"James","family":"Walsh","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,3,15]]},"reference":[{"key":"968_CR1","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1007\/BF01621472","volume":"30","author":"W Buchholz","year":"1991","unstructured":"Buchholz, W.: Notation systems for infinitary derivations. Arch. Math. Logic 30, 277\u2013296 (1991)","journal-title":"Arch. Math. Logic"},{"key":"968_CR2","unstructured":"Feferman, S.: The continuum hypothesis is neither a definite mathematical problem nor a definite logical problem. preprint, (2014)"},{"key":"968_CR3","volume-title":"Proof Theory and Logical Complexity","author":"J-Y Girard","year":"1987","unstructured":"Girard, J.-Y.: Proof Theory and Logical Complexity, vol. 1. Bibliopolis, Naples (1987)"},{"key":"968_CR4","volume-title":"Slicing the Truth: On the Computable and Reverse Mathematics of Combinatorial Principles","author":"DR Hirschfeldt","year":"2015","unstructured":"Hirschfeldt, D.R.: Slicing the Truth: On the Computable and Reverse Mathematics of Combinatorial Principles. World Scientific, Singapore (2015)"},{"key":"968_CR5","first-page":"95","volume-title":"Lectures on Modern Mathematics","author":"G Kreisel","year":"1965","unstructured":"Kreisel, G.: Mathematical logic. In: Saaty, T.L. (ed.) Lectures on Modern Mathematics, pp. 95\u2013195. Wiley, New York (1965)"},{"issue":"2","key":"968_CR6","doi-asserted-by":"publisher","first-page":"575","DOI":"10.2178\/jsl\/1305810765","volume":"76","author":"A Marcone","year":"2011","unstructured":"Marcone, A., Montalb\u00e1n, A.: The Veblen functions for computability theorists. J. Symbol. Logic 76(2), 575\u2013602 (2011)","journal-title":"J. Symbol. Logic"},{"key":"968_CR7","doi-asserted-by":"publisher","first-page":"1350","DOI":"10.1017\/jsl.2020.9","volume":"86","author":"F Pakhomov","year":"2020","unstructured":"Pakhomov, F., Walsh, J.: Reflection ranks and ordinal analysis. J. Symbol. Logic 86, 1350\u20131384 (2020)","journal-title":"J. Symbol. Logic"},{"key":"968_CR8","first-page":"209","volume-title":"Handbook of Proof Theory","author":"W Pohlers","year":"1998","unstructured":"Pohlers, W.: Subsystems of set theory and second order number theory. In: Buss, S.R. (ed.) Handbook of Proof Theory, pp. 209\u2013335. Elsevier, Hoboken (1998)"},{"key":"968_CR9","doi-asserted-by":"crossref","unstructured":"Schmerl, U.R.: A fine structure generated by reflection formulas over primitive recursive arithmetic. In: Studies in Logic and the Foundations of Mathematics, Logic Colloquium, vol. 97, pp. 335\u2013350. Elsevier (1979)","DOI":"10.1016\/S0049-237X(08)71633-1"},{"key":"968_CR10","doi-asserted-by":"crossref","unstructured":"Schwichtenberg, H.: Proof theory: some applications of cut-elimination. In: Studies in Logic and the Foundations of Mathematics, Handbook of Mathematical Logic, vol.\u00a090, pp. 867\u2013895. Elsevier (1977)","DOI":"10.1016\/S0049-237X(08)71124-8"},{"key":"968_CR11","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511581007","volume-title":"Subsystems of Second Order Arithmetic","author":"SG Simpson","year":"2009","unstructured":"Simpson, S.G.: Subsystems of Second Order Arithmetic. Cambridge University Press, Cambridge (2009)"},{"key":"968_CR12","unstructured":"Walsh, J.: On the hierarchy of natural theories. arXiv preprint arXiv:2106.05794 (2021)"},{"issue":"1","key":"968_CR13","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1017\/jsl.2022.64","volume":"89","author":"J Walsh","year":"2024","unstructured":"Walsh, J.: An incompleteness theorem via ordinal analysis. J. Symbol. Logic 89(1), 80\u201396 (2024)","journal-title":"J. Symbol. Logic"}],"container-title":["Archive for Mathematical Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-025-00968-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s00153-025-00968-3\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s00153-025-00968-3.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,14]],"date-time":"2025-10-14T17:01:46Z","timestamp":1760461306000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s00153-025-00968-3"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,3,15]]},"references-count":13,"journal-issue":{"issue":"7-8","published-print":{"date-parts":[[2025,11]]}},"alternative-id":["968"],"URL":"https:\/\/doi.org\/10.1007\/s00153-025-00968-3","relation":{},"ISSN":["0933-5846","1432-0665"],"issn-type":[{"value":"0933-5846","type":"print"},{"value":"1432-0665","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,3,15]]},"assertion":[{"value":"29 April 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"26 February 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 March 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"}}]}}