{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T11:26:17Z","timestamp":1773401177132,"version":"3.50.1"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We provide a much shorter proof of the following partition theorem of P. Erd\u0151s and R. Rado: If $X$ is an uncountable linear order into which neither $\\omega_1$ nor $\\omega_1^{*}$ embeds, then $X \\to (\\alpha, 4)^{3}$ for every ordinal $\\alpha  &lt;  \\omega + \\omega$.  We also provide two counterexamples to possible generalizations of this theorem, one of which answers a question of E. C. Milner and K. Prikry.<\/jats:p>","DOI":"10.37236\/1502","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:05:14Z","timestamp":1578708314000},"source":"Crossref","is-referenced-by-count":3,"title":["A short proof of a partition relation for triples"],"prefix":"10.37236","volume":"7","author":[{"given":"Albin L.","family":"Jones","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2000,3,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r24\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v7i1r24\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:24:46Z","timestamp":1579325086000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v7i1r24"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000,3,11]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2000,1,1]]}},"URL":"https:\/\/doi.org\/10.37236\/1502","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2000,3,11]]},"article-number":"R24"}}