{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,25]],"date-time":"2026-04-25T07:18:01Z","timestamp":1777101481814,"version":"3.51.4"},"reference-count":6,"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":1288,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2010,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>We show, relative to the base theory RCA<jats:sub>0<\/jats:sub>: A nontrivial tree satisfies Ramsey's Theorem only if it is biembeddable with the complete binary tree. There is a class of partial orderings for which Ramsey's Theorem for pairs is equivalent to ACA<jats:sub>0<\/jats:sub>. Ramsey's Theorem for singletons for the complete binary tree is stronger than <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200002474_inline1\"\/>. hence stronger than Ramsey's Theorem for singletons for \u03c9. These results lead to extensions of results, or answers to questions, of Chubb, Hirst, and McNicholl [3].<\/jats:p>","DOI":"10.2178\/jsl\/1278682209","type":"journal-article","created":{"date-parts":[[2010,7,9]],"date-time":"2010-07-09T09:30:45Z","timestamp":1278667845000},"page":"945-954","source":"Crossref","is-referenced-by-count":13,"title":["Reverse mathematics and Ramsey's property for trees"],"prefix":"10.1017","volume":"75","author":[{"given":"Jared","family":"Corduan","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marcia J.","family":"Groszek","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Joseph R.","family":"Mileti","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200002474_ref005","unstructured":"Hirst J. , personal communication (e-mail 06 12, 2008)."},{"key":"S0022481200002474_ref001","first-page":"1","volume":"66","author":"Cholak","year":"2001","journal-title":"On the strength of Ramsey's theorem for pairs"},{"key":"S0022481200002474_ref003","first-page":"201","volume":"74","author":"Chubb","year":"2009","journal-title":"Reverse mathematics, computability, and partitions of trees"},{"key":"S0022481200002474_ref004","unstructured":"Hirst J. , Combinatorics in subsystems of second order arithmetic, Ph.D. thesis, The Pennsylvania State University, 1987."},{"key":"S0022481200002474_ref002","first-page":"797","volume":"63","author":"Chong","year":"1998","journal-title":"\u03a32 induction and infinite injury priority argument, I. Maximal sets and the jump operator"},{"key":"S0022481200002474_ref006","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-59971-2"}],"container-title":["The Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200002474","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,27]],"date-time":"2019-04-27T17:39:16Z","timestamp":1556386756000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200002474\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,9]]},"references-count":6,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2010,9]]}},"alternative-id":["S0022481200002474"],"URL":"https:\/\/doi.org\/10.2178\/jsl\/1278682209","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,9]]}}}