Block combinatorics

Farmaki, V.; Negrepontis, S.

doi:10.1090/S0002-9947-06-03864-5

Block combinatorics
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by V. Farmaki and S. Negrepontis PDF

Trans. Amer. Math. Soc. 358 (2006), 2759-2779 Request permission

Abstract:

In this paper we extend the block combinatorics partition theorems of Hindman and Milliken-Taylor in the setting of the recursive system of the block Schreier families $(\mathcal {B}^\xi )$, 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 the Milliken-Taylor 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.

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