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Proceedings of the American Mathematical Society

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A brief remark on van der Waerden spaces


Author: Albin L. Jones
Journal: Proc. Amer. Math. Soc. 132 (2004), 2457-2460
MSC (2000): Primary 03E50, 05C55, 54F65, 11P99
Published electronically: March 24, 2004
MathSciNet review: 2052425
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Abstract: We demonstrate that Martin's axiom for $\sigma$-centered notions of forcing implies the existence of a van der Waerden space that is not a Hindman space. Our proof is an adaptation of the one given by M. Kojman and S. Shelah that such a space exists if one assumes the continuum hypothesis to be true.


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Additional Information

Albin L. Jones
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045-2142
Email: alj@math.ku.edu

DOI: https://doi.org/10.1090/S0002-9939-04-07351-4
Keywords: General topology, continuum hypothesis, Martin's axiom, van der Waerden space, Hindman space, arithmetic sequence, convergent sequence
Received by editor(s): March 13, 2003
Received by editor(s) in revised form: April 30, 2003
Published electronically: March 24, 2004
Additional Notes: We would like to thank both the University of Kansas for its support of this research and the anonymous referee for his helpful comments and suggestions.
Communicated by: Alan Dow
Article copyright: © Copyright 2004 Albin L. Jones