  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.
