{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,13]],"date-time":"2026-05-13T14:23:22Z","timestamp":1778682202761,"version":"3.51.4"},"reference-count":10,"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":5124,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2000,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>It is consistent that there is a set mapping from the four-tuples of \u03c9<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>into the finite subsets with no free subsets of size<jats:italic>t<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>for some natural number<jats:italic>t<\/jats:italic><jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>. For any<jats:italic>n<\/jats:italic>&lt; \u03c9 it is consistent that there is a set mapping from the pairs of \u03c9<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>into the finite subsets with no infinite free sets. For any<jats:italic>n<\/jats:italic>&lt; \u03c9 it is consistent that there is a set mapping from the pairs of \u03c9<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>into \u03c9<jats:sub><jats:italic>n<\/jats:italic><\/jats:sub>with no uncountable free sets.<\/jats:p>","DOI":"10.2307\/2586540","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:01:31Z","timestamp":1146938491000},"page":"333-338","source":"Crossref","is-referenced-by-count":7,"title":["Two consistency results on set mappings"],"prefix":"10.1017","volume":"65","author":[{"given":"P\u00e9ter","family":"Komj\u00e1th","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Saharon","family":"Shelah","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200012500_ref010","first-page":"23","article-title":"Une g\u00e9n\u00e9ralisation d'un th\u00e9or\u00e8me de M. Sierpi\u0144ski","volume":"5","author":"Ruziewicz","year":"1936","journal-title":"Publications Math\u00e9matiques de l'Universit\u00e9 de Belgrade"},{"key":"S0022481200012500_ref002","doi-asserted-by":"publisher","DOI":"10.1007\/BF02023868"},{"key":"S0022481200012500_ref007","first-page":"304","volume":"56","author":"Komj\u00c1th","year":"1991","journal-title":"A set mapping with no infinite free subsets"},{"key":"S0022481200012500_ref001","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9939-1950-0035809-8"},{"key":"S0022481200012500_ref009","doi-asserted-by":"crossref","first-page":"5","DOI":"10.4064\/fm-29-1-5-8","article-title":"Sur un probl\u00e8me de M. Ruziewicz de la th\u00c9orie des relations","volume":"29","author":"Piccard","year":"1937","journal-title":"Fundamenta Mathematicae"},{"key":"S0022481200012500_ref005","doi-asserted-by":"publisher","DOI":"10.4064\/fm-50-2-123-128"},{"key":"S0022481200012500_ref008","doi-asserted-by":"publisher","DOI":"10.4064\/fm-38-1-14-17"},{"key":"S0022481200012500_ref006","first-page":"347","volume-title":"Logic Colloquium '73, Bristol","author":"Hajnal","year":"1975"},{"key":"S0022481200012500_ref003","volume-title":"Combinatorial set theory: Partition relations for cardinals","author":"Erd\u00f6s","year":"1984"},{"key":"S0022481200012500_ref004","first-page":"51","article-title":"Egy halmazelm\u00e9leti t\u00e9telr\u0151l","volume":"44","author":"Gr\u00fcnwald","year":"1937","journal-title":"Mathematikai \u00c9s Fizikai Lapok"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200012500","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,7,26]],"date-time":"2021-07-26T20:10:03Z","timestamp":1627330203000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200012500\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,3]]},"references-count":10,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2000,3]]}},"alternative-id":["S0022481200012500"],"URL":"https:\/\/doi.org\/10.2307\/2586540","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,3]]}}}