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ISSN 1088-6826(e) ISSN 0002-9939(p)

A brief remark on van der Waerden spaces

Author(s): Albin L. Jones
Journal: Proc. Amer. Math. Soc. 132 (2004), 2457-2460.
MSC (2000): Primary 03E50, 05C55, 54F65, 11P99
Posted: 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.

References:

1.: Murray G. Bell, On the combinatorial principle ${P}(\mathfrak{c})$ , Fund. Math. 114 (1981), no. 2, 149-157. MR 83e:03077
2.: H. Furstenberg and B. Weiss, Topological dynamics and combinatorial number theory, J. Analyse Math. 34 (1978), 61-85 (1979). MR 80g:05009
3.: Neil Hindman, Finite sums from sequences within cells of a partition of , J. Combinatorial Theory Ser. A 17 (1974), 1-11. MR 50:2067
4.: T. Jech, Set theory, Pure and Applied Mathematics, Academic Press [Harcourt Brace Jovanovich Publishers], New York, 1978. MR 80a:03062
5.: M. Kojman, Hindman spaces, Proc. Amer. Math. Soc. 130 (2002), no. 6, 1597-1602. MR 2003c:54068
6.: M. Kojman and S. Shelah, Van der Waerden spaces and Hindman spaces are not the same, Proc. Amer. Math. Soc. 131 (2003), no. 5, 1619-1622. MR 2004c:54003
7.: Menachem Kojman, Van der Waerden spaces, Proc. Amer. Math. Soc. 130 (2002), no. 3, 631-635 (electronic). MR 2002i:54018
8.: K. Kunen, Set theory: An introduction to independence proofs, reprint of the 1980 original, North-Holland Publishing Co., Amsterdam, 1983. MR 85e:03003
9.: B. L. van der Waerden, Beweis eine Baudetschen Vermutung, Nieuw Arch. Wisk. 15 (1927), 212-216.

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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: 10.1090/S0002-9939-04-07351-4
PII: S 0002-9939(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
Posted: 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
Copyright of article: Copyright 2004, Albin L. Jones

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