Hindman's theorem

From Polymath1Wiki
Revision as of 15:25, 15 February 2009 by Teorth (Talk | contribs)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

Hindman's theorem: If [math][2]^\omega := \bigcup_{n=0}^\infty [2]^n[/math] is finitely colored, then one of the color classes contain an infinite-dimensional combinatorial subspace, i.e. another copy of [math][2]^\omega[/math].

The generalization of this theorem to higher k is the Carlson-Simpson theorem.