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In particular, this cell must contain a sequence and all of its finite sums, and another sequence and all of its finite products, a fact that was previously known only by utilizing the algebraic structure of the Stone\u2013\u010cech compactification \u03b2\u2115 of \u2115.<\/jats:p>","DOI":"10.1017\/s0963548300000638","type":"journal-article","created":{"date-parts":[[2008,9,12]],"date-time":"2008-09-12T11:18:58Z","timestamp":1221218338000},"page":"221-241","source":"Crossref","is-referenced-by-count":14,"title":["Additive and Multiplicative Ramsey Theorems in \u2115 \u2013 Some Elementary Results"],"prefix":"10.1017","volume":"2","author":[{"given":"Vitaly","family":"Bergelson","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Neil","family":"Hindman","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2008,9,12]]},"reference":[{"key":"S0963548300000638_ref009","doi-asserted-by":"publisher","DOI":"10.1007\/BF02813304"},{"key":"S0963548300000638_ref006","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9904-1977-14316-4"},{"key":"S0963548300000638_ref010","doi-asserted-by":"publisher","DOI":"10.1515\/9781400855162"},{"key":"S0963548300000638_ref019","doi-asserted-by":"publisher","DOI":"10.1007\/BF01188632"},{"key":"S0963548300000638_ref003","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(88)90073-8"},{"key":"S0963548300000638_ref004","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1990-0982232-5"},{"key":"S0963548300000638_ref002","doi-asserted-by":"publisher","DOI":"10.1016\/0097-3165(86)90074-9"},{"key":"S0963548300000638_ref005","doi-asserted-by":"crossref","unstructured":"[5] Blass A. , Hirst J. and Simpson S. 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