{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,30]],"date-time":"2026-04-30T07:38:18Z","timestamp":1777534698056,"version":"3.51.4"},"reference-count":4,"publisher":"Wiley","issue":"4-5","license":[{"start":{"date-parts":[[2004,8,18]],"date-time":"2004-08-18T00:00:00Z","timestamp":1092787200000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[2004,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>A theorem published by A. Grzegorczyk in 1955 states a certain kind of effective uniform continuity of computable functionals whose values are natural numbers and whose arguments range over the total functions in the set of the natural numbers and over the natural numbers. Namely, for any such functional a computable functional with one function\u2010argument and the same number\u2010arguments exists such that the values of the first of the functionals at functions dominated by a given one are completely determined by their restrictions to numbers not exceeding the corresponding values of the second functional at the given function. We prove versions of this theorem for the class of the primitive recursive functionals and for the class of the elementary recursive ones. Analogous results can be proved for many other subrecursive classes of functionals. (\u00a9 2004 WILEY\u2010VCH Verlag GmbH &amp; Co. KGaA, Weinheim)<\/jats:p>","DOI":"10.1002\/malq.200310117","type":"journal-article","created":{"date-parts":[[2004,8,18]],"date-time":"2004-08-18T12:02:13Z","timestamp":1092830533000},"page":"520-524","source":"Crossref","is-referenced-by-count":1,"title":["Some subrecursive versions of Grzegorczyk's Uniformity Theorem"],"prefix":"10.1002","volume":"50","author":[{"given":"Dimiter","family":"Skordev","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2004,8,18]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","first-page":"168","DOI":"10.4064\/fm-42-1-168-202","article-title":"Computable functionals","volume":"42","author":"Grzegorczyk A.","year":"1955","journal-title":"Fund. Math."},{"key":"e_1_2_1_3_2","first-page":"1","article-title":"A simple example of an unsolvable arithmetical problem (in Hungarian)","volume":"50","author":"Kalm\u00e1r L.","year":"1943","journal-title":"Matematikai \u00e9s Fizikai Lapok"},{"key":"e_1_2_1_4_2","unstructured":"S. C.Kleene Introduction to Metamathematics (D. van Nostrand New York\u2010Toronto 1952)."},{"key":"e_1_2_1_5_2","first-page":"275","article-title":"A note on computable functionals","volume":"59","author":"Keene S. C.","year":"1956","journal-title":"Nederl. Acad. Wet., Proc. Ser. A"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.200310117","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.200310117","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,8,30]],"date-time":"2023-08-30T16:13:55Z","timestamp":1693412035000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.200310117"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,8,18]]},"references-count":4,"journal-issue":{"issue":"4-5","published-print":{"date-parts":[[2004,9]]}},"alternative-id":["10.1002\/malq.200310117"],"URL":"https:\/\/doi.org\/10.1002\/malq.200310117","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,8,18]]}}}