{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T14:41:50Z","timestamp":1776696110925,"version":"3.51.2"},"reference-count":2,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":14072,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1975,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Sacks [2] has asked whether there exists a uniform solution to Post's problem, i.e. an enumeration operation <jats:italic>W<\/jats:italic> such that <jats:italic>d<\/jats:italic> &lt; <jats:italic>W(d)<\/jats:italic> &lt; <jats:italic>d<\/jats:italic>\u2032 for every degree <jats:italic>d<\/jats:italic>. It is shown here that if such an operation <jats:italic>W<\/jats:italic> exists it cannot itself in a particular technical sense be uniform. In fact, the jump operation is characterized amongst such uniform enumeration operations by the condition: <jats:italic>d<\/jats:italic> &lt; <jats:italic>W(d)<\/jats:italic> for all <jats:italic>d<\/jats:italic>. In addition, it is proved that the only other uniform enumeration operations such that <jats:italic>d<\/jats:italic> \u2264 <jats:italic>W(d)<\/jats:italic> for all <jats:italic>d<\/jats:italic> are those which equal the identity operation above some fixed degree.<\/jats:p>","DOI":"10.2307\/2272164","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:36:35Z","timestamp":1146951395000},"page":"401-409","source":"Crossref","is-referenced-by-count":10,"title":["Uniform enumeration operations"],"prefix":"10.1017","volume":"40","author":[{"given":"A. H.","family":"Lachlan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200053019_ref001","volume-title":"Theory of recursive functions and effective computability","author":"Rogers","year":"1967"},{"key":"S0022481200053019_ref002","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1967-0207558-7"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200053019","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,29]],"date-time":"2019-05-29T19:22:00Z","timestamp":1559157720000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200053019\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1975,9]]},"references-count":2,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1975,9]]}},"alternative-id":["S0022481200053019"],"URL":"https:\/\/doi.org\/10.2307\/2272164","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1975,9]]}}}