This is an announcement for the paper "Block combinatorics" by V. Farmaki and S. Negrepontis.

Abstract: 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 (B^xi) 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.

Archive classification: Combinatorics; Functional Analysis

Mathematics Subject Classification: 05D10; 46B20

Remarks: 26 pages, AMS-LaTeX

The source file(s), fn04.tex: 83752 bytes, is(are) stored in gzipped form as 0406188.gz with size 20kb. The corresponding postcript file has gzipped size 98kb.

Submitted from: combs@mail.ma.utexas.edu

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