{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,25]],"date-time":"2023-10-25T21:22:25Z","timestamp":1698268945232},"reference-count":10,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":12885,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1978,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We study the measure independent character of G\u00f6del speed-up theorems, in particular, we strengthen Arbib's necessary condition for the occurrence of a G\u00f6del speed-up [2, p. 13] to an equivalence result and generalize Di Paola's speed-up theorem [4]. We also characterize undecidable theories as precisely those theories which possess consistent measure independent G\u00f6del speed-ups and show that a theory \u03c4<jats:sub>2<\/jats:sub> is a measure independent G\u00f6del speed-up of a theory \u03c4<jats:sub>1<\/jats:sub> if and only if the set of undecidable sentences of \u03c4<jats:sub>1<\/jats:sub> which are provable in \u03c4<jats:sub>2<\/jats:sub> is not recursively enumerable.<\/jats:p>","DOI":"10.2307\/2273506","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:48:57Z","timestamp":1146952137000},"page":"667-672","source":"Crossref","is-referenced-by-count":4,"title":["Some results on measure independent G\u00f6del speed-ups"],"prefix":"10.1017","volume":"43","author":[{"given":"Martin K.","family":"Solomon","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200049185_ref001","first-page":"23","article-title":"Uber die L\u00e4nge der Beweise","volume":"VII","author":"G\u00f6del","year":"1936","journal-title":"Ergeb, eines mathematischen Kolloquiums"},{"key":"S0022481200049185_ref007","doi-asserted-by":"publisher","DOI":"10.4064\/fm-41-2-203-271"},{"key":"S0022481200049185_ref002","first-page":"6","volume-title":"Automata theory","author":"Arbib","year":"1966"},{"key":"S0022481200049185_ref003","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1971-12696-4"},{"key":"S0022481200049185_ref004","first-page":"398","volume":"40","author":"Di Paola","year":"1975","journal-title":"A theorem on shortening the length of proof in formal systems of arithmetic"},{"key":"S0022481200049185_ref005","volume-title":"Computability and unsolvability","author":"Davis","year":"1958"},{"key":"S0022481200049185_ref010","doi-asserted-by":"publisher","DOI":"10.1145\/321386.321395"},{"key":"S0022481200049185_ref009","unstructured":"Solomon M. K. , The G\u00f6del speed-up phenomenon, Doctoral Dissertation, Stevens Institute of Technology, 1975."},{"key":"S0022481200049185_ref006","first-page":"87","volume-title":"Computational complexity","author":"Davis","year":"1973"},{"key":"S0022481200049185_ref008","volume-title":"Theory of recursive functions and effective computability","author":"Rogers","year":"1967"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200049185","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,27]],"date-time":"2019-05-27T19:08:03Z","timestamp":1558984083000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200049185\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1978,12]]},"references-count":10,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1978,12]]}},"alternative-id":["S0022481200049185"],"URL":"https:\/\/doi.org\/10.2307\/2273506","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1978,12]]}}}