{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,10]],"date-time":"2026-03-10T15:50:22Z","timestamp":1773157822919,"version":"3.50.1"},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"3","license":[{"start":{"date-parts":[[2014,3,12]],"date-time":"2014-03-12T00:00:00Z","timestamp":1394582400000},"content-version":"unspecified","delay-in-days":192,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2013,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We compare the strength of polychromatic and monochromatic Ramsey theory in several set-theoretic domains. We show that the rainbow Ramsey theorem does not follow from ZF, nor does the rainbow Ramsey theorem imply Ramsey's theorem over ZF. Extending the classical result of Erd\u0151s and Rado we show that the axiom of choice precludes the natural infinite exponent partition relations for polychromatic Ramsey theory. We introduce rainbow Ramsey ultrafilters, a polychromatic analogue of the usual Ramsey ultrafilters. We investigate the relationship of rainbow Ramsey ultrafilters with various special classes of ultrafilters, showing for example that every rainbow Ramsey ultrafilter is nowhere dense but rainbow Ramsey ultrafilters need not be rapid. This entails comparison of the polychromatic and monochromatic Ramsey theorems as combinatorial principles on <jats:italic>\u03c9<\/jats:italic>.<\/jats:p>","DOI":"10.2178\/jsl.7803130","type":"journal-article","created":{"date-parts":[[2014,1,6]],"date-time":"2014-01-06T18:18:22Z","timestamp":1389032302000},"page":"951-968","source":"Crossref","is-referenced-by-count":2,"title":["Comparisons of Polychromatic and Monochromatic Ramsey Theory"],"prefix":"10.1017","volume":"78","author":[{"given":"Justin","family":"Palumbo","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200126684_ref008","doi-asserted-by":"publisher","DOI":"10.1016\/j.disc.2004.02.013"},{"key":"S0022481200126684_ref006","first-page":"1310","volume":"74","author":"Csima","year":"2009","journal-title":"The strength of the rainbow Ramsey theorem"},{"key":"S0022481200126684_ref010","volume-title":"The higher infinite","author":"Kanamori","year":"2003"},{"key":"S0022481200126684_ref012","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100053032"},{"key":"S0022481200126684_ref002","first-page":"199","article-title":"On sub-Ramsey numbers","volume":"22","author":"Alspach","year":"1986","journal-title":"Ars Combinatorial"},{"key":"S0022481200126684_ref001","first-page":"865","volume":"72","author":"Abraham","year":"2007","journal-title":"Some results in polychromatic Ramsey theory"},{"key":"S0022481200126684_ref005","doi-asserted-by":"publisher","DOI":"10.1007\/BF02780177"},{"key":"S0022481200126684_ref014","doi-asserted-by":"publisher","DOI":"10.2307\/1999642"},{"key":"S0022481200126684_ref009","volume-title":"The axiom of choice","volume":"75","author":"Jech","year":"1973"},{"key":"S0022481200126684_ref013","first-page":"305","volume-title":"Logic Colloquium '95","volume":"11","author":"Shelah","year":"1998"},{"key":"S0022481200126684_ref004","first-page":"387","volume":"42","author":"Blass","year":"1977","journal-title":"Ramsey's theorem in the hierarchy of choice principles"},{"key":"S0022481200126684_ref011","first-page":"205","volume":"34","author":"Kleinberg","year":"1969","journal-title":"The independence of Ramsey's theorem"},{"key":"S0022481200126684_ref003","first-page":"624","volume":"60","author":"Baumgartner","year":"1995","journal-title":"Ultrafilters on \u03c9"},{"key":"S0022481200126684_ref007","first-page":"113","volume-title":"10th Asian Logic Conference","author":"Fla\u0161kov\u00e1","year":"2010"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200126684","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,23]],"date-time":"2019-04-23T19:56:52Z","timestamp":1556049412000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200126684\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,9]]},"references-count":14,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2013,9]]}},"alternative-id":["S0022481200126684"],"URL":"https:\/\/doi.org\/10.2178\/jsl.7803130","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,9]]}}}