# Sh:781

- Kojman, M., & Shelah, S. (2003).
*van der Waerden spaces and Hindman spaces are not the same*. Proc. Amer. Math. Soc.,**131**(5), 1619–1622. arXiv: math/0112265 DOI: 10.1090/S0002-9939-02-06916-2 MR: 1950294 -
Abstract:

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. - published version (4p)

Bib entry

@article{Sh:781, author = {Kojman, Menachem and Shelah, Saharon}, title = {{van der Waerden spaces and Hindman spaces are not the same}}, journal = {Proc. Amer. Math. Soc.}, fjournal = {Proceedings of the American Mathematical Society}, volume = {131}, number = {5}, year = {2003}, pages = {1619--1622}, issn = {0002-9939}, doi = {10.1090/S0002-9939-02-06916-2}, mrclass = {54A20 (03E35 03E50)}, mrnumber = {1950294}, mrreviewer = {E. Todd Eisworth}, doi = {10.1090/S0002-9939-02-06916-2}, note = {\href{https://arxiv.org/abs/math/0112265}{arXiv: math/0112265}}, arxiv_number = {math/0112265} }