Hindman's theorem: Difference between revisions
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New page: '''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 subspac... |
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'''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>. | '''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]]. | The generalization of this theorem to higher k is the [[Carlson-Simpson theorem]]. Hindman's theorem also implies [[Folkman's theorem]]. | ||
Revision as of 23:45, 15 February 2009
Hindman's theorem: If [math]\displaystyle{ [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]\displaystyle{ [2]^\omega }[/math].
The generalization of this theorem to higher k is the Carlson-Simpson theorem. Hindman's theorem also implies Folkman's theorem.
