{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,4,19]],"date-time":"2024-04-19T10:46:06Z","timestamp":1713523566470},"reference-count":6,"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":3663,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2004,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Assuming CH. Hindman [2] showed that the existence of certain ultrafilters on the power set of the natural numbers is equivalent to Hindman's Theorem. Adapting this work to a countable setting formalized in RCA<jats:sub>0<\/jats:sub>, this article proves the equivalence of the existence of certain ultrafilters on countable Boolean algebras and an iterated form of Hindman's Theorem, which is closely related to Milliken's Theorem. A computable restriction of Hindman's Theorem follows as a corollary.<\/jats:p>","DOI":"10.2178\/jsl\/1080938825","type":"journal-article","created":{"date-parts":[[2005,3,2]],"date-time":"2005-03-02T21:25:13Z","timestamp":1109798713000},"page":"65-72","source":"Crossref","is-referenced-by-count":6,"title":["Hindman's theorem, ultrafilters, and reverse mathematics"],"prefix":"10.1017","volume":"69","author":[{"given":"Jeffry L.","family":"Hirst","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200008008_ref001","doi-asserted-by":"publisher","DOI":"10.1090\/conm\/065\/891245"},{"key":"S0022481200008008_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(74)90023-5"},{"key":"S0022481200008008_ref002","first-page":"341","article-title":"The existence of certain ultra-filters on N and a conjecture of Graham and Rothschild","volume":"36","author":"Hindman","year":"1972","journal-title":"Proceedings of the American Mathematical Society"},{"key":"S0022481200008008_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-59971-2"},{"key":"S0022481200008008_ref005","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(75)90039-4"},{"key":"S0022481200008008_ref004","unstructured":"Hirst Jeffry L. , Combinatorics in subsystems of second order arithmetic, Ph.D. thesis , The Pennsylvania State University, 1987."}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200008008","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,6]],"date-time":"2019-05-06T21:28:24Z","timestamp":1557178104000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200008008\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,3]]},"references-count":6,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2004,3]]}},"alternative-id":["S0022481200008008"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1080938825","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2004,3]]}}}