{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,11]],"date-time":"2025-07-11T10:41:09Z","timestamp":1752230469380},"reference-count":6,"publisher":"Wiley","issue":"3","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":4334,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1995,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>The remainder set <jats:italic>A<\/jats:italic>\u27c2<jats:italic>B<\/jats:italic> of a set of sentences <jats:italic>A<\/jats:italic> modulo a set of sentences <jats:italic>B<\/jats:italic> is the set of all maximal subsets of <jats:italic>A<\/jats:italic> not implying any element of <jats:italic>B.<\/jats:italic> A remainder equation is an expression containing remainder sets, such as {<jats:italic>A<\/jats:italic>} = <jats:italic>B<\/jats:italic>\u27c2<jats:italic>X<\/jats:italic>, in which at least one set is unknown. Solutions to some classes of remainder equations are reported, and some unsolved problems are listed.<\/jats:p>","DOI":"10.1002\/malq.19950410307","type":"journal-article","created":{"date-parts":[[2007,5,26]],"date-time":"2007-05-26T17:46:40Z","timestamp":1180201600000},"page":"362-368","source":"Crossref","is-referenced-by-count":4,"title":["Some Solved and Unsolved Remainder Equations"],"prefix":"10.1002","volume":"41","author":[{"given":"Sven Ove","family":"Hansson","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":"10.1007\/978-94-009-8484-4_5"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.2307\/2274239"},{"key":"e_1_2_1_4_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00370186"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00666230"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.2307\/2275221"},{"key":"e_1_2_1_7_2","article-title":"Kernel contraction","author":"Hansson S. O.","journal-title":"J. Symbolic Logic"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19950410307","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19950410307","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T14:46:00Z","timestamp":1698331560000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19950410307"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,1]]},"references-count":6,"journal-issue":{"issue":"3","published-print":{"date-parts":[[1995,1]]}},"alternative-id":["10.1002\/malq.19950410307"],"URL":"https:\/\/doi.org\/10.1002\/malq.19950410307","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,1]]}}}