{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,6]],"date-time":"2025-08-06T13:12:43Z","timestamp":1754485963868},"reference-count":7,"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":4394,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2002,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We give a model-theoretic proof of the fact that for all infinite Abelian groups <jats:italic>P \u2260 NP<\/jats:italic> in the sense of binary nondeterminism. This result has been announced 1994 by Christine Ga\u00dfner.<\/jats:p>","DOI":"10.2178\/jsl\/1190150041","type":"journal-article","created":{"date-parts":[[2007,12,13]],"date-time":"2007-12-13T14:12:10Z","timestamp":1197555130000},"page":"235-238","source":"Crossref","is-referenced-by-count":9,"title":["A model-theoretic proof for <i>P \u2260 NP<\/i> over all infinite abelian group"],"prefix":"10.1017","volume":"67","author":[{"given":"Mihai","family":"Prunescu","sequence":"first","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200009968_ref005","volume-title":"Mathematical Logic Quarterly","author":"Hemmerling"},{"key":"S0022481200009968_ref003","doi-asserted-by":"publisher","DOI":"10.1090\/S0273-0979-1989-15750-9"},{"key":"S0022481200009968_ref006","doi-asserted-by":"publisher","DOI":"10.1006\/jcom.1993.1023"},{"key":"S0022481200009968_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-0701-6"},{"key":"S0022481200009968_ref001","unstructured":"Asser G\u00fcnter , Ga\u00dfner Christine , and Prunescu Mihai , F\u00fcr alle unendlichen abelschen Gruppen G ist P(G) \u2260 NP(G). (drei Beweise), preprint der Universit\u00e4t Greifswald, January 2000."},{"key":"S0022481200009968_ref007","volume-title":"Lespetits cailloux","author":"Poizat","year":"1995"},{"key":"S0022481200009968_ref004","doi-asserted-by":"crossref","unstructured":"Bourgade Menard , Separations et transferts dans la hierarchie polynomiale des groupes abeliens infinis, preprint, 2000.","DOI":"10.1002\/1521-3870(200111)47:4<493::AID-MALQ493>3.0.CO;2-S"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200009968","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,6]],"date-time":"2019-05-06T21:34:28Z","timestamp":1557178468000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200009968\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,3]]},"references-count":7,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2002,3]]}},"alternative-id":["S0022481200009968"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1190150041","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2002,3]]}}}