{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T14:19:14Z","timestamp":1775053154381,"version":"3.50.1"},"reference-count":11,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":5430,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1992,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let \u2203<jats:sup><jats:italic>n<\/jats:italic><\/jats:sup> denote the set of all formulas \u2203<jats:italic>x<\/jats:italic><jats:sub>1<\/jats:sub>\u2026\u2203<jats:italic>x<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>[<jats:italic>P<\/jats:italic>(<jats:italic>x<\/jats:italic><jats:sub>1<\/jats:sub>, \u2026,<jats:italic>x<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>) = 0], where <jats:italic>P<\/jats:italic> is a polynomial with integer coefficients. We prove a new relation\u2010combining theorem from which it follows that if \u2203<jats:sup><jats:italic>n<\/jats:italic><\/jats:sup> is undecidable over N, then \u2203<jats:sup>2<jats:italic>n<\/jats:italic>+2<\/jats:sup> is undecidable over Z.<\/jats:p>","DOI":"10.1002\/malq.19920380117","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T05:44:51Z","timestamp":1180417491000},"page":"209-212","source":"Crossref","is-referenced-by-count":3,"title":["ANEW RELATION\u2010COMBINING THEOREM AND ITS APPLICATION"],"prefix":"10.1002","volume":"38","author":[{"given":"Zhi\u2010Wei","family":"Sun","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.1968.0010"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.2307\/2273588"},{"key":"e_1_2_1_4_2","first-page":"279","article-title":"Enumerable sets are diophantine","volume":"191","author":"Matijasevi\u010d Ju. V.","year":"1970","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"e_1_2_1_5_2","first-page":"770","article-title":"A Diophantine representation of the set of prime numbers","volume":"196","author":"Matijasevi\u010d Ju. V.","year":"1971","journal-title":"Dokl. Akad. Nauk SSSR"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-010-1138-9_7"},{"key":"e_1_2_1_7_2","doi-asserted-by":"crossref","first-page":"521","DOI":"10.4064\/aa-27-1-521-553","article-title":"Reduction of an arbitrary diophantine equation to one in 13 unknowns","volume":"27","author":"Matijasevi\u010d Ju. V.","year":"1975","journal-title":"Acta Arith."},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.2307\/2032501"},{"key":"e_1_2_1_9_2","first-page":"257","article-title":"Reduction of unknowns in Diophantine representations","volume":"35","author":"Sun Zhi\u2010Wei","year":"1992","journal-title":"Science in China (Ser. A)"},{"key":"e_1_2_1_10_2","article-title":"Jones' work on Hilbert's tenth problem and related topics\u2014Dedicated to Prof. Jones for his visiting China","author":"Sun Zhi\u2010Wei","journal-title":"Adv. in Math. (China)"},{"key":"e_1_2_1_11_2","doi-asserted-by":"crossref","first-page":"203","DOI":"10.4099\/math1924.11.203","article-title":"On weak number theories","volume":"11","author":"Tung S. P.","year":"1985","journal-title":"Japan. J. Math."},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(87)90013-7"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19920380117","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19920380117","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T20:36:02Z","timestamp":1695846962000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19920380117"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,1]]},"references-count":11,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1992,1]]}},"alternative-id":["10.1002\/malq.19920380117"],"URL":"https:\/\/doi.org\/10.1002\/malq.19920380117","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1992,1]]}}}