{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T12:55:10Z","timestamp":1785416110352,"version":"3.56.0"},"reference-count":11,"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":23638,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1949,6,23]]},"abstract":"<jats:p>In this paper, we are concerned with the arithmetical definability of certain notions of integers and rationals in terms of other notions. The results derived will be applied to obtain a negative solution of corresponding decision problems.<\/jats:p><jats:p>In Section 1, we show that addition of positive integers can be defined arithmetically in terms of multiplication and the unary operation of successor<jats:italic>S<\/jats:italic>(where<jats:italic>Sa<\/jats:italic>=<jats:italic>a<\/jats:italic>+ 1). Also, it is shown that both addition and multiplication can be defined arithmetically in terms of successor and the relation of divisibility | (where<jats:italic>x|y<\/jats:italic>means<jats:italic>x<\/jats:italic>divides<jats:italic>y<\/jats:italic>).<\/jats:p>","DOI":"10.2307\/2266510","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T19:05:25Z","timestamp":1146942325000},"page":"98-114","source":"Crossref","is-referenced-by-count":180,"title":["Definability and decision problems in arithmetic"],"prefix":"10.1017","volume":"14","author":[{"given":"Julia","family":"Robinson","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200072650_ref010","first-page":"261","article-title":"Der Wahrheitsbegri\ufb00 in den formalisierten Sprachen","volume":"1","author":"Tarski","year":"1935","journal-title":"Studia philosophica"},{"key":"S0022481200072650_ref009","first-page":"87","volume":"1","author":"Rosser","year":"1936","journal-title":"Extensions of some theorems of G\u00f6del and Church"},{"key":"S0022481200072650_ref011","first-page":"176","volume":"4","author":"Tarski","year":"1939","journal-title":"New investigations on the completeness of deductive theories (abstract)"},{"key":"S0022481200072650_ref008","volume-title":"Comptes rendus du I Congris des Pays Slaves","author":"Presburger","year":"1929"},{"key":"S0022481200072650_ref007","first-page":"249","article-title":"Un nouveau syst\u00e8me irr\u00e9ductible de postulats pour l'alg\u00e8bre","author":"Padoa","year":"1902","journal-title":"Comptes rendus du 2-e Congr\u00e8s International des Math\u00e9maticiens"},{"key":"S0022481200072650_ref006","unstructured":"Hilbert D. , and Bernays P. , Grundlagen der Mathematik."},{"key":"S0022481200072650_ref002","doi-asserted-by":"publisher","DOI":"10.2307\/2371045"},{"key":"S0022481200072650_ref001","doi-asserted-by":"publisher","DOI":"10.1215\/S0012-7094-47-01439-7"},{"key":"S0022481200072650_ref003","first-page":"40","volume":"1","author":"Church","year":"1936","journal-title":"A note on the Entscheidungsproblem"},{"key":"S0022481200072650_ref005","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1515\/crll.1923.152.129","article-title":"\u00dcber die Darstellbarkeit von Zahlen durch quadratische Formen im K\u00f6rper der rationalen Zahlen","volume":"152","author":"Hasse","year":"1923","journal-title":"Journal f\u00fcr die reine und angewandte Mathematik"},{"key":"S0022481200072650_ref004","doi-asserted-by":"publisher","DOI":"10.1007\/BF01700692"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200072650","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,4]],"date-time":"2024-02-04T07:21:08Z","timestamp":1707031268000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200072650\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1949,6,23]]},"references-count":11,"journal-issue":{"issue":"2","published-print":{"date-parts":[[1949,6,23]]}},"alternative-id":["S0022481200072650"],"URL":"https:\/\/doi.org\/10.2307\/2266510","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1949,6,23]]}}}