{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,4]],"date-time":"2022-04-04T18:08:07Z","timestamp":1649095687068},"reference-count":11,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2021,3,26]],"date-time":"2021-03-26T00:00:00Z","timestamp":1616716800000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2021,6]]},"abstract":"Abstract<\/jats:title>We introduce and study a natural class of fields in which certain first-order definable sets are existentially definable, and characterise this class by a number of equivalent conditions. We show that global fields belong to this class, and in particular obtain a number of new existential (or diophantine) predicates over global fields.<\/jats:p>","DOI":"10.1017\/jsl.2021.28","type":"journal-article","created":{"date-parts":[[2021,3,26]],"date-time":"2021-03-26T04:56:11Z","timestamp":1616734571000},"page":"701-708","update-policy":"http:\/\/dx.doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["A CLASS OF FIELDS WITH A RESTRICTED MODEL COMPLETENESS PROPERTY"],"prefix":"10.1017","volume":"86","author":[{"given":"PHILIP","family":"DITTMANN","sequence":"first","affiliation":[]},{"given":"DION","family":"LEIJNSE","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2021,3,26]]},"reference":[{"key":"S0022481221000281_r6","volume-title":"Field Arithmetic","volume":"11","author":"Fried","year":"2008"},{"key":"S0022481221000281_r9","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-22174-7_4"},{"key":"S0022481221000281_r3","unstructured":"[3] Dittmann, P. , A model-theoretic approach to the arithmetic of global fields , Ph.D. thesis, University of Oxford, 2018. Available at https:\/\/ora.ox.ac.uk\/objects\/uuid:c798e052-b305-4cca-8964-e7959e486a5d."},{"key":"S0022481221000281_r5","doi-asserted-by":"publisher","DOI":"10.1007\/BF01388493"},{"key":"S0022481221000281_r10","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1980-0583852-6"},{"key":"S0022481221000281_r2","doi-asserted-by":"publisher","DOI":"10.1112\/S0010437X17007977"},{"key":"S0022481221000281_r4","first-page":"147","volume-title":"Logic Colloquium \u201978","volume":"97","author":"van den Dries","year":"1979"},{"key":"S0022481221000281_r11","first-page":"412","article-title":"Notes on the stability of separably closed fields","volume":"44","author":"Wood","year":"1979","journal-title":"Journal"},{"key":"S0022481221000281_r1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-34395-0"},{"key":"S0022481221000281_r8","volume-title":"Algebra","author":"Lang","year":"1993"},{"key":"S0022481221000281_r7","volume-title":"A Shorter Model Theory","author":"Hodges","year":"1997"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481221000281","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,2,18]],"date-time":"2022-02-18T11:17:18Z","timestamp":1645183038000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481221000281\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,26]]},"references-count":11,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2021,6]]}},"alternative-id":["S0022481221000281"],"URL":"https:\/\/doi.org\/10.1017\/jsl.2021.28","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,26]]},"assertion":[{"value":"\u00a9 The Association for Symbolic Logic 2021","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}}]}}