{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,3,31]],"date-time":"2022-03-31T11:25:50Z","timestamp":1648725950979},"reference-count":2,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":18547,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1963,6]]},"abstract":"<jats:p>In Smullyan [1], where recursive enumerability is defined in terms of elementary dyadic arithmetics (dyadic EA's), it is shown that for any number <jats:italic>n<\/jats:italic>, the parallel definition in terms of <jats:italic>n<\/jats:italic>-adic EA\u2032s is equivalent. This proof at one stage uses the deep result of Godei that plus and times form a sub-basis for the recursively enumerable attributes (sets and relations)<jats:sup>2<\/jats:sup>. The aim of this note is to prove this equivalence in more pedestrian fashion.<\/jats:p>","DOI":"10.2307\/2271598","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T16:21:15Z","timestamp":1146932475000},"page":"161-163","source":"Crossref","is-referenced-by-count":0,"title":["On n-adic representation of numbers"],"prefix":"10.1017","volume":"28","author":[{"given":"Thomas E.","family":"Patton","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200115269_ref001","doi-asserted-by":"crossref","unstructured":"Smullyan R. M. , Theory of formal systems, Annals of mathematics studies, no. 47 (1961).","DOI":"10.1515\/9781400882007"},{"key":"S0022481200115269_ref002","article-title":"Extended canonical systems","volume":"12","author":"Smullyan","year":"1961","journal-title":"Proceedings of the American Mathematicae Society,"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200115269","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,4]],"date-time":"2019-06-04T15:22:57Z","timestamp":1559661777000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200115269\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1963,6]]},"references-count":2,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1963,6]]}},"alternative-id":["S0022481200115269"],"URL":"https:\/\/doi.org\/10.2307\/2271598","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1963,6]]}}}