2004/06/09 by Vassiliki Farmaki, V. Farmaki, Farmaki, V. +2
Engineering · Mathematics · #05D10 #46B20 #Combinatorics (math.CO) #FOS: Mathematics #Functional Analysis (math.FA) #graph theory and CDMA systems #math.CO #math.FA #msc:05D10 #msc:46B20
paper · pdf · doi:10.48550/arxiv.math/0406188
26 pages, AMS-LaTeX
arxiv created 2004/06/09 · openalex publication_date 2004/06/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we extend the block combinatorics partition theorems of Hindman and Milliken in the setting of the recursive system of the block Schreier families (Bxi) consisting of families defined for every countable ordinal xi. Results contain (a) a block partition Ramsey theorem for every countable ordinal xi (Hindman's theorem corresponding to xi=1, and Milliken's theorem to xi a finite ordinal), (b) a countable ordinal form of the block Nash-Williams partition theorem, and (c) a countable ordinal block partition theorem for sets closed in the infinite block analogue of Ellentuck's topology.