{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,29]],"date-time":"2023-10-29T06:10:47Z","timestamp":1698559847542},"reference-count":19,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,11,13]],"date-time":"2006-11-13T00:00:00Z","timestamp":1163376000000},"content-version":"vor","delay-in-days":3603,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematical Logic Qtrly"],"published-print":{"date-parts":[[1997,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We describe sets of partial Boolean functions being closed under the operations of superposition. For any class <jats:italic>A<\/jats:italic> of total functions we define the set \ud835\udd10(<jats:italic>A<\/jats:italic>) consisting of all partial classes which contain precisely the functions of <jats:italic>A<\/jats:italic> as total functions. The cardinalities of such sets \ud835\udd10(<jats:italic>A<\/jats:italic>) can be finite or infinite. We state some general results on \ud835\udd10(<jats:italic>A<\/jats:italic>). In particular, we describe all 30 closed sets of partial Boolean functions which contain all monotone and zero\u2010preserving total Boolean functions.<\/jats:p>","DOI":"10.1002\/malq.19970430407","type":"journal-article","created":{"date-parts":[[2007,5,30]],"date-time":"2007-05-30T01:28:01Z","timestamp":1180488481000},"page":"510-524","source":"Crossref","is-referenced-by-count":11,"title":["On Partial Classes Containig All Monotone and Zero\u2010Preserving Total Boolean Functions"],"prefix":"10.1002","volume":"43","author":[{"given":"Birger","family":"Strauch","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,11,13]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"crossref","unstructured":"B\u00f6rner F. L.Haddad andR.P\u00f6schel Minimal partial clones. 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Preprint1995."}],"container-title":["Mathematical Logic Quarterly"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fmalq.19970430407","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/malq.19970430407","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,28]],"date-time":"2023-10-28T02:08:33Z","timestamp":1698458913000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/malq.19970430407"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997,1]]},"references-count":19,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1997,1]]}},"alternative-id":["10.1002\/malq.19970430407"],"URL":"https:\/\/doi.org\/10.1002\/malq.19970430407","archive":["Portico"],"relation":{},"ISSN":["0942-5616","1521-3870"],"issn-type":[{"value":"0942-5616","type":"print"},{"value":"1521-3870","type":"electronic"}],"subject":[],"published":{"date-parts":[[1997,1]]}}}