{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,11]],"date-time":"2023-10-11T06:10:21Z","timestamp":1697004621443},"reference-count":3,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":3603,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1997,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let \u2138 be the set of G\u00f6del numbers Gn(<jats:italic>f<\/jats:italic>) of function symbols <jats:italic>f<\/jats:italic> such that <jats:bold>PRA<\/jats:bold> \u22a2 and let \u03b3 be the function such that <jats:disp-formula>\n\n<\/jats:disp-formula>\nWe prove: (1) The r. e. set \u2138 is m\u2010complete; (2) the function \u03b3 is not primitive recursive in any class of functions {<jats:italic>f<\/jats:italic><jats:sub>1<\/jats:sub>, <jats:italic>f<\/jats:italic><jats:sub>2<\/jats:sub>, \u20db} so long as each <jats:italic>f<jats:sub>i<\/jats:sub><\/jats:italic> has a recursive upper bound. This implies that \u03b3 is not primitive recursive in \u2138 although it is recursive in \u2138.<\/jats:p>","DOI":"10.1002\/malq.19970430305","type":"journal-article","created":{"date-parts":[[2007,5,30]],"date-time":"2007-05-30T08:49:29Z","timestamp":1180514969000},"page":"328-332","source":"Crossref","is-referenced-by-count":0,"title":["On the Difficulty of Writing Out formal Proofs in Arithmetic"],"prefix":"10.1002","volume":"43","author":[{"given":"Ryo","family":"Kashima","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Takeshi","family":"Yamaguchi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Classical Recursion Theory","author":"Odifreddi P.","year":"1989"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8601-8"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19970430106"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19970430305","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19970430305","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,10]],"date-time":"2023-10-10T05:37:41Z","timestamp":1696916261000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19970430305"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,1]]},"references-count":3,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1997,1]]}},"alternative-id":["10.1002\/malq.19970430305"],"URL":"https:\/\/doi.org\/10.1002\/malq.19970430305","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997,1]]}}}