{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,3]],"date-time":"2022-04-03T00:32:56Z","timestamp":1648945976537},"reference-count":5,"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":11699,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[1982,3]]},"abstract":"<jats:p><jats:italic>Q<jats:sub>\u03ba<\/jats:sub><\/jats:italic><jats:italic>\u03bb<\/jats:italic>. <jats:italic>P<jats:sub>\u03ba<\/jats:sub><\/jats:italic><jats:italic>\u03bb<\/jats:italic> the space of all &lt; <jats:italic>\u03ba<\/jats:italic>-sized subsets of <jats:italic>\u03bb<\/jats:italic>, has provided numerous opportunities for the gainful employment of set theorists in recent years, thanks to its combinatorial richness and to its relationships with various large cardinals. In the spirit of <jats:italic>P<jats:sub>\u03ba<\/jats:sub><\/jats:italic><jats:italic>\u03bb<\/jats:italic> we offer the following definition:<\/jats:p><jats:p>For <jats:italic>\u03ba<\/jats:italic> \u2264 <jats:italic>\u03bb<\/jats:italic> both cardinals, <jats:italic>Q<jats:sub>\u03ba<\/jats:sub><\/jats:italic><jats:italic>\u03bb<\/jats:italic> is the set of all partitions of <jats:italic>\u03bb<\/jats:italic> into &lt; <jats:italic>\u03ba<\/jats:italic>-many pieces (an element of <jats:italic>q<\/jats:italic> \u2208 <jats:italic>Q<jats:sub>\u03ba<\/jats:sub><\/jats:italic><jats:italic>\u03bb<\/jats:italic> is called a piece of <jats:italic>q<\/jats:italic>). Equivalently<\/jats:p><jats:p><jats:disp-formula><jats:graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" orientation=\"portrait\" mime-subtype=\"gif\" mimetype=\"image\" position=\"float\" xlink:type=\"simple\" xlink:href=\"S0022481200044765_eqnU01\" \/><\/jats:disp-formula><\/jats:p><jats:p>An element of <jats:italic>P<jats:sub>\u03ba<\/jats:sub><\/jats:italic><jats:italic>\u03bb<\/jats:italic> may be viewed as an injection from a &lt; <jats:italic>\u03ba<\/jats:italic>-sized set into <jats:italic>\u03bb<\/jats:italic>, with some information thrown away. An element of <jats:italic>Q<jats:sub>\u03ba<\/jats:sub><\/jats:italic><jats:italic>\u03bb<\/jats:italic> is a surjection from <jats:italic>\u03bb<\/jats:italic> onto a &lt; <jats:italic>\u03ba<\/jats:italic>-sized set, with analogous loss of information.<\/jats:p><jats:p>For <jats:italic>p, q<\/jats:italic> \u2208 <jats:italic>Q<jats:sub>\u03ba<\/jats:sub><\/jats:italic><jats:italic>\u03bb<\/jats:italic>, we say <jats:italic>p<\/jats:italic> \u2264 <jats:italic>q<\/jats:italic> iff <jats:italic>q<\/jats:italic> is a refinement of <jats:italic>p<\/jats:italic> (every piece of <jats:italic>q<\/jats:italic> is contained in a piece of <jats:italic>p<\/jats:italic>).<\/jats:p>","DOI":"10.2307\/2273387","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T21:58:32Z","timestamp":1146952712000},"page":"137-146","source":"Crossref","is-referenced-by-count":1,"title":["Ultrafilters on spaces of partitions"],"prefix":"10.1017","volume":"47","author":[{"given":"James M.","family":"Henle","sequence":"first","affiliation":[]},{"given":"William S.","family":"Zwicker","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200044765_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(78)90031-1"},{"key":"S0022481200044765_ref004","volume-title":"Lecture Notes in Mathematics","volume":"612","author":"Kleinberg","year":"1977"},{"key":"S0022481200044765_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(79)90024-X"},{"key":"S0022481200044765_ref001","unstructured":"Blass A. , Orderings of ultrafilters, Doctoral Dissertation, Harvard University, 1970."},{"key":"S0022481200044765_ref002","unstructured":"Henle J. M. , Aspects of choiceless combinatorial set theory, Doctoral Dissertation, Massachusetts Institute of Technology, 1976."}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200044765","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,24]],"date-time":"2019-05-24T21:43:00Z","timestamp":1558734180000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200044765\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,3]]},"references-count":5,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1982,3]]}},"alternative-id":["S0022481200044765"],"URL":"https:\/\/doi.org\/10.2307\/2273387","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,3]]}}}