{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T01:14:57Z","timestamp":1648948497016},"reference-count":6,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":8046,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1992,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We give necessary conditions for a set to be definable by a formula with a universal quantifier and an existential quantifier over algebraic integer rings or algebraic number fields. From these necessary conditions we obtain some undefinability results. For example, <jats:bold>N<\/jats:bold> is not definable by such a formula over <jats:bold>Z<\/jats:bold>. This extends a previous result of R. M. Robinson.<\/jats:p>","DOI":"10.2307\/2275172","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:43:45Z","timestamp":1146941025000},"page":"1-11","source":"Crossref","is-referenced-by-count":0,"title":["Arithmetic definability by formulas with two quantifiers"],"prefix":"10.1017","volume":"57","author":[{"given":"Shih Ping","family":"Tung","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200023136_ref003","doi-asserted-by":"publisher","DOI":"10.3998\/mpub.9690541"},{"key":"S0022481200023136_ref004","doi-asserted-by":"crossref","first-page":"203","DOI":"10.4099\/math1924.11.203","article-title":"On weak number theories","volume":"11","author":"Tung","year":"1985","journal-title":"Japanese Journal of Mathematics, New Series"},{"key":"S0022481200023136_ref002","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1951-0041080-4"},{"key":"S0022481200023136_ref005","first-page":"152","volume":"52","author":"Tung","year":"1987","journal-title":"Definability in number fields"},{"key":"S0022481200023136_ref006","doi-asserted-by":"publisher","DOI":"10.1002\/malq.19880340203"},{"key":"S0022481200023136_ref001","doi-asserted-by":"publisher","DOI":"10.1112\/jlms\/s2-18.3.385"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200023136","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,16]],"date-time":"2019-05-16T18:32:23Z","timestamp":1558031543000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200023136\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,3]]},"references-count":6,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1992,3]]}},"alternative-id":["S0022481200023136"],"URL":"https:\/\/doi.org\/10.2307\/2275172","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,3]]}}}