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A remark on incomparable ultrafilters in the Rudin-Keisler order

Author: Eva Butkovičová
Journal: Proc. Amer. Math. Soc. 112 (1991), 577-578
MSC: Primary 04A20; Secondary 03E05
MathSciNet review: 1045131
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Abstract: If $ {2^{ < {\mathbf{c}}}} > {\mathbf{c}}$ and $ p$ is an ultrafilter on $ \omega $ of character $ {\mathbf{c}}$ then there exist many ultrafilters that are incomparable with $ p$ in the Rudin-Keisler order.

References [Enhancements On Off] (What's this?)

  • [HvM] K. P. Hart and J. van Mill, Open problems on $ \beta \omega $, Problems in Topology (to appear). MR 1078643
  • [H] N. Hindman, Is there a point of $ {\omega ^*}$ that sees all others?, Proc. Amer. Math. Soc. 104 (1988), 1235-1238. MR 931732 (89d:04008)
  • [vM] J. van Mill, An introduction to $ \beta \omega $, Handbook of Set-Theoretic Topology (K. Kunen and J. E. Vaughan, eds.), North-Holland, Amsterdam, 1984, pp. 504-568. MR 776619 (85k:54001)

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Keywords: Ultrafilters, Rudin-Keisler order
Article copyright: © Copyright 1991 American Mathematical Society

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