{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,22]],"date-time":"2026-07-22T16:40:24Z","timestamp":1784738424700,"version":"3.55.0"},"reference-count":23,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,6,1]],"date-time":"2026-06-01T00:00:00Z","timestamp":1780272000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T00:00:00Z","timestamp":1778716800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Information and Computation"],"published-print":{"date-parts":[[2026,6]]},"DOI":"10.1016\/j.ic.2026.105476","type":"journal-article","created":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T00:01:27Z","timestamp":1778889687000},"page":"105476","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":1,"special_numbering":"C","title":["The arithmetic hierarchy of real functions"],"prefix":"10.1016","volume":"311","author":[{"given":"Cole","family":"Wyeth","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Marcus","family":"Hutter","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"1","key":"10.1016\/j.ic.2026.105476_bib0001","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1002\/1521-3870(200101)47:1<51::AID-MALQ51>3.0.CO;2-W","article-title":"The arithmetical hierarchy of real numbers","volume":"47","author":"Zheng","year":"2001","journal-title":"Math. Logic Q."},{"issue":"1","key":"10.1016\/j.ic.2026.105476_bib0002","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1007\/s00224-006-1343-6","article-title":"Real Hypercomputation and Continuity","volume":"41","author":"Ziegler","year":"2007","journal-title":"Theory Comput. Syst."},{"key":"10.1016\/j.ic.2026.105476_bib0003","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/j.entcs.2006.08.015","article-title":"Revising Type-2 Computation and Degrees of Discontinuity","volume":"167","author":"Ziegler","year":"2007","journal-title":"Electron. Notes Theor. Comput. Sci."},{"issue":"1","key":"10.1016\/j.ic.2026.105476_bib0004","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1002\/malq.200310125","article-title":"Effective Borel measurability and reducibility of functions","volume":"51","author":"Brattka","year":"2005","journal-title":"Math. Logic Q."},{"key":"10.1016\/j.ic.2026.105476_bib0005","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1016\/j.tcs.2017.11.020","article-title":"On the computability of Solomonoff induction and AIXI","volume":"716","author":"Leike","year":"2018","journal-title":"Theor. Comput. Sci."},{"key":"10.1016\/j.ic.2026.105476_bib0006","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-56999-9","article-title":"Computable Analysis: An Introduction","author":"Weihrauch","year":"2000"},{"issue":"1","key":"10.1016\/j.ic.2026.105476_bib0007","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/S0304-3975(98)00045-0","article-title":"Computability on continuous, lower semi-continuous and upper semi-continuous real functions","volume":"234","author":"Weihrauch","year":"2000","journal-title":"Theor. Comput. Sci."},{"issue":"3","key":"10.1016\/j.ic.2026.105476_bib0008","first-page":"1","article-title":"A Galois connection between Turing jumps and limits","volume":"14","author":"Brattka","year":"2018","journal-title":"Logical Methods Comput. Sci."},{"issue":"12","key":"10.1016\/j.ic.2026.105476_bib0009","doi-asserted-by":"crossref","first-page":"4639","DOI":"10.4171\/jems\/1289","article-title":"The foundations of spectral computations via the Solvability Complexity Index hierarchy","volume":"25","author":"Colbrook","year":"2022","journal-title":"J. Eur. Math. Soc."},{"key":"10.1016\/j.ic.2026.105476_bib0010","series-title":"Proceedings Of The 11Th Asian Logic Conference: In Honor of Professor Chong Chitat on His 60th Birthday","first-page":"59","article-title":"Limitwise monotonic functions and their applications","author":"Downey","year":"2012"},{"issue":"9","key":"10.1016\/j.ic.2026.105476_bib0011","doi-asserted-by":"crossref","first-page":"3275","DOI":"10.1090\/S0002-9939-2013-11586-8","article-title":"Limitwise Monotonic Sequences and Degree Spectra of Structures","volume":"141","author":"Kalimullin","year":"2013","journal-title":"Proc. Am. Math. Soc."},{"issue":"3","key":"10.1016\/j.ic.2026.105476_bib0012","doi-asserted-by":"crossref","first-page":"321","DOI":"10.1016\/0304-3975(77)90048-2","article-title":"A fundamental effect in computations on real numbers","volume":"5","author":"Luckhardt","year":"1977","journal-title":"Theor. Comput. Sci."},{"key":"10.1016\/j.ic.2026.105476_bib0013","series-title":"Universal Artificial Intelligence: Sequential Decisions based on Algorithmic Probability","author":"Hutter","year":"2005"},{"issue":"1","key":"10.1016\/j.ic.2026.105476_bib0014","doi-asserted-by":"crossref","first-page":"41","DOI":"10.1090\/S0002-9947-1943-0007371-8","article-title":"Recursive Predicates and Quantifiers","volume":"53","author":"Kleene","year":"1943","journal-title":"Trans. Am. Math. Soc."},{"key":"10.1016\/j.ic.2026.105476_bib0015","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-12898-5","article-title":"Recursion-Theoretic Hierarchies","author":"Hinman","year":"1978"},{"key":"10.1016\/j.ic.2026.105476_bib0016","unstructured":"J. Rute, Are these two definitions of arithmetical hierarchy of real numbers equivalent?, 2016, https:\/\/mathoverflow.net\/q\/235302. version: 2016-04-04."},{"issue":"4-5","key":"10.1016\/j.ic.2026.105476_bib0017","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1002\/malq.200710005","article-title":"Primitive recursive real numbers","volume":"53","author":"Chen","year":"2007","journal-title":"Math. Logic Q."},{"issue":"3","key":"10.1016\/j.ic.2026.105476_bib0018","doi-asserted-by":"crossref","first-page":"644","DOI":"10.2307\/1970028","article-title":"On degrees of unsolvability","volume":"69","author":"Shoenfield","year":"1959","journal-title":"Ann. Math."},{"issue":"1","key":"10.1016\/j.ic.2026.105476_bib0019","doi-asserted-by":"crossref","first-page":"28","DOI":"10.2307\/2270580","article-title":"Limiting recursion","volume":"30","author":"Gold","year":"1965","journal-title":"J. Symb. Logic"},{"key":"10.1016\/j.ic.2026.105476_bib0020","series-title":"2015 30th Annual ACM\/IEEE Symposium on Logic in Computer Science","first-page":"438","article-title":"Descriptive set theory in the category of represented spaces","author":"Pauly","year":"2015"},{"issue":"8","key":"10.1016\/j.ic.2026.105476_bib0021","doi-asserted-by":"crossref","first-page":"1414","DOI":"10.1017\/S0960129516000128","article-title":"A comparison of concepts from computable analysis and effective descriptive set theory","volume":"27","author":"Gregoriades","year":"2017","journal-title":"Math. Struct. Comput. Sci."},{"issue":"2","key":"10.1016\/j.ic.2026.105476_bib0022","doi-asserted-by":"crossref","first-page":"170","DOI":"10.1017\/bsl.2023.16","article-title":"Computably compact metric spaces","volume":"29","author":"Downey","year":"2023","journal-title":"Bull. Symb. Logic"},{"issue":"07","key":"10.1016\/j.ic.2026.105476_bib0023","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1090\/S0273-0979-1989-15750-9","article-title":"On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines","volume":"21","author":"Blum","year":"1989","journal-title":"Bull. Amer. Math. Soc."}],"container-title":["Information and Computation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0890540126000738?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0890540126000738?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,6]],"date-time":"2026-07-06T22:28:20Z","timestamp":1783376900000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0890540126000738"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,6]]},"references-count":23,"alternative-id":["S0890540126000738"],"URL":"https:\/\/doi.org\/10.1016\/j.ic.2026.105476","relation":{},"ISSN":["0890-5401"],"issn-type":[{"value":"0890-5401","type":"print"}],"subject":[],"published":{"date-parts":[[2026,6]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"The arithmetic hierarchy of real functions","name":"articletitle","label":"Article Title"},{"value":"Information and Computation","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.ic.2026.105476","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Author(s). Published by Elsevier Inc.","name":"copyright","label":"Copyright"}],"article-number":"105476"}}