{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T22:36:23Z","timestamp":1781562983076,"version":"3.54.5"},"reference-count":16,"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":4940,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. symb. log."],"published-print":{"date-parts":[[2000,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Suppose that <jats:italic>\u03b1<\/jats:italic> = <jats:italic>\u03b3<\/jats:italic> + <jats:italic>\u03b4<\/jats:italic> where <jats:italic>\u03b3<\/jats:italic> \u2265 <jats:italic>\u03b4<\/jats:italic> &gt; 0. Then there is a graph <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200011750_inline1\"\/> which has no independent set of order type <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S0022481200011750_inline2\"\/> and has no pentagram (a pentagram is a set of five points with all pairs joined by edges). In the notation of Erd\u0151s and Rado. who generalized Ramsey's Theorem to this setting.<\/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=\"S0022481200011750_Uequ1\"\/><\/jats:disp-formula><\/jats:p>","DOI":"10.2307\/2586684","type":"journal-article","created":{"date-parts":[[2006,5,6]],"date-time":"2006-05-06T18:02:41Z","timestamp":1146938561000},"page":"969-978","source":"Crossref","is-referenced-by-count":3,"title":["An ordinal partition avoiding pentagrams"],"prefix":"10.1017","volume":"65","author":[{"given":"Jean A.","family":"Larson","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2014,3,12]]},"reference":[{"key":"S0022481200011750_ref013","first-page":"264\u2013286","article-title":"On a problem of formal logic","volume":"30","author":"Ramsey","year":"1930","journal-title":"Proceedings of the London Mathematical Society 2"},{"key":"S0022481200011750_ref001","first-page":"5\u201317","volume-title":"Set theory audits applications (Toronto, ON, 1987)","volume":"1401","author":"Baumgartner","year":"1989"},{"key":"S0022481200011750_ref012","unstructured":"Milner E.C. , Some combinatorial problems in set theory, Ph.D. thesis , London, 1962."},{"key":"S0022481200011750_ref007","first-page":"17\u201348","volume-title":"Axiomatic set theory (University of California, Los Angeles, CA, 1967)","volume":"13","author":"Erd\u0151s","year":"1971"},{"key":"S0022481200011750_ref003","unstructured":"Darby C. , private communication."},{"key":"S0022481200011750_ref008","doi-asserted-by":"publisher","DOI":"10.4153\/CMB-1972-088-1"},{"key":"S0022481200011750_ref015","first-page":"302\u2013314","article-title":"Teilmengen von Mengen mil Relationen","volume":"31","author":"Specker","year":"1957","journal-title":"Comment. Math. Helv."},{"key":"S0022481200011750_ref011","doi-asserted-by":"publisher","DOI":"10.1016\/0003-4843(73)90006-5"},{"key":"S0022481200011750_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(72)90105-7"},{"key":"S0022481200011750_ref014","unstructured":"Schipperus R. , Countable partition ordinals, Ph.D. thesis , University of Colorado, Boulder, 1999."},{"key":"S0022481200011750_ref009","unstructured":"Galvin F. , Circulated lecture notes, University of Colorado, 1971."},{"key":"S0022481200011750_ref005","unstructured":"Darby C. and Larson J. , A positive partition relationfor a critical countable ordinal, in preparation."},{"key":"S0022481200011750_ref010","doi-asserted-by":"publisher","DOI":"10.4064\/fm-82-4-357-361"},{"key":"S0022481200011750_ref016","volume-title":"Combinatorial set theory","author":"Williams","year":"1977"},{"key":"S0022481200011750_ref004","doi-asserted-by":"publisher","DOI":"10.1006\/jctb.1999.1903"},{"key":"S0022481200011750_ref006","first-page":"223\u2013228","volume-title":"Logic and combinatorics (Areata, CA, 1985)","volume":"65","author":"Erd\u0151s","year":"1987"}],"container-title":["Journal of Symbolic Logic"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0022481200011750","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,8]],"date-time":"2019-05-08T20:47:21Z","timestamp":1557348441000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0022481200011750\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,9]]},"references-count":16,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2000,9]]}},"alternative-id":["S0022481200011750"],"URL":"https:\/\/doi.org\/10.2307\/2586684","relation":{},"ISSN":["0022-4812","1943-5886"],"issn-type":[{"value":"0022-4812","type":"print"},{"value":"1943-5886","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,9]]}}}