van der Waerden spaces and Hindman spaces are not the same

by Kojman and Shelah. [KjSh:781]
Proc American Math Soc, 2003
A Hausdorff topological space X is van der Waerden if for every sequence (x_n)_n in X there is a converging subsequence (x_n)_{n in A} where A subseteq omega contains arithmetic progressions of all finite lengths. A Hausdorff topological space X is Hindman if for every sequence (x_n)_n in X there is an IP-converging subsequence (x_n)_{n in FS(B)} for some infinite B subseteq omega . We show that the continuum hypothesis implies the existence of a van der Waerden space which is not Hindman.


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