{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,25]],"date-time":"2026-06-25T02:51:11Z","timestamp":1782355871906,"version":"3.54.5"},"reference-count":13,"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>We prove that any binary relation with underlying set (base) <jats:italic>E<\/jats:italic> with cardinality <jats:italic>n<\/jats:italic> &gt; 6 is reconstructible from its restrictions of cardinality 2, 3, 4 and (<jats:italic>n<\/jats:italic> \u2010 1). In part I we characterize relations <jats:italic>R<\/jats:italic> and <jats:italic>R<\/jats:italic>' on the same base <jats:italic>E<\/jats:italic> such that <jats:italic>R\/X<\/jats:italic> and <jats:italic>R'\/X<\/jats:italic> are isomorphic for every subset <jats:italic>X<\/jats:italic> of <jats:italic>E<\/jats:italic> with cardinality 2, 3, 4. In part II we shall prove that <jats:italic>R<\/jats:italic> and <jats:italic>R<\/jats:italic>' are isomorphic as soon as <jats:italic>n<\/jats:italic> &gt; 6 when <jats:italic>R\/X<\/jats:italic> and <jats:italic>R\/X<\/jats:italic>' are isomorphic for every subset <jats:italic>X<\/jats:italic> of <jats:italic>E<\/jats:italic> with cardinality 2, 3, 4 and (<jats:italic>n<\/jats:italic> \u2010 1).<\/jats:p>","DOI":"10.1002\/malq.19920380104","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T05:46:51Z","timestamp":1180417611000},"page":"27-37","source":"Crossref","is-referenced-by-count":24,"title":["RECONSTRUCTION OF BINARY RELATIONS FROM THEIR RESTRICTIONS OF CARDINALITY 2, 3, 4 and (<i>n<\/i> \u2010 1) I"],"prefix":"10.1002","volume":"38","author":[{"given":"G\u00e9rard","family":"Lopez","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Claire","family":"Rauzy","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190010306"},{"key":"e_1_2_1_3_2","first-page":"203","article-title":"Abritement entre relations et sp\u00e9cialement entre cha\u00eenes","volume":"5","author":"Fra\u00efss\u00e9 R.","year":"1970","journal-title":"Symposia Math. Inst. Naz. Alte Math."},{"key":"e_1_2_1_4_2","volume-title":"Theory of Relations","author":"Fra\u00efss\u00e9 R.","year":"1987"},{"key":"e_1_2_1_5_2","unstructured":"Fra\u00efss\u00e9 R. andG.Lopez La reconstruction d'une relation dans l'hypoth\u00e8se forte. Presses de l'Universit\u00e9 de Montreal. To appear."},{"key":"e_1_2_1_6_2","first-page":"47","volume-title":"Theory of Graphs and its Applications","author":"Harary F.","year":"1964"},{"key":"e_1_2_1_7_2","first-page":"577","article-title":"La reconstructibilit\u00e9 des tournois sans diamants","volume":"306","author":"Gnanvo C.","year":"1988","journal-title":"C. R. Acad. Sci. Paris"},{"key":"e_1_2_1_8_2","first-page":"303","article-title":"L'ind\u00e9formabilit\u00e9 des relations et multirelations binaires","volume":"24","author":"Lopez G.","year":"1978","journal-title":"This Zeitschrift"},{"key":"e_1_2_1_9_2","first-page":"639","article-title":"La (n \u2010 4)\u2010reconstructibilit\u00e9 des tournois de cardinalit\u00e9 > 9","volume":"307","author":"Lopez G.","year":"1988","journal-title":"C. R. Acad. Sci. Paris"},{"key":"e_1_2_1_10_2","first-page":"697","article-title":"Reconstructibilit\u00e9 des relations binaires par des familles de leurs restrictions","volume":"307","author":"Lopez G.","year":"1988","journal-title":"C. R. Acad. Sci. Paris"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF01215230"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190010108"},{"key":"e_1_2_1_13_2","unstructured":"Stockmeyer P. K. A census of non\u2010reconstructible digraphs six related families J. Combinatorial Theory Series B21 223\u2013239."},{"key":"e_1_2_1_14_2","volume-title":"A Collection of Mathematical Problems","author":"Ulam S. M.","year":"1960"}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19920380104","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19920380104","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T20:36:38Z","timestamp":1695846998000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19920380104"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1992,1]]},"references-count":13,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1992,1]]}},"alternative-id":["10.1002\/malq.19920380104"],"URL":"https:\/\/doi.org\/10.1002\/malq.19920380104","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]]}}}