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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
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Abstract:
We demonstrate that Martin's axiom for  -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:
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 , 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.
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- 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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