Selective ultrafilters and $\omega \rightarrow (\omega )^\omega$
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- by Todd Eisworth PDF
- Proc. Amer. Math. Soc. 127 (1999), 3067-3071 Request permission
Abstract:
Mathias (Happy families, Ann. Math. Logic. 12 (1977), 59–111) proved that, assuming the existence of a Mahlo cardinal, it is consistent that CH holds and every set of reals in $L(\mathbb {R})$ is $\mathcal {U}$-Ramsey with respect to every selective ultrafilter $\mathcal {U}$. In this paper, we show that the large cardinal assumption cannot be weakened.References
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Additional Information
- Todd Eisworth
- Affiliation: Institute of Mathematics, The Hebrew Univeristy, Jerusalem, Israel
- Email: eisworth@math.huji.ac.il
- Received by editor(s): December 29, 1995
- Received by editor(s) in revised form: December 10, 1997
- Published electronically: April 23, 1999
- Additional Notes: This research is part of the author’s Ph.D. dissertation written at the University of Michigan under the supervision of Professor Andreas Blass. The author would like to thank the referee for his tips on streamlining the proof.
- Communicated by: Andreas R. Blass
- © Copyright 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 3067-3071
- MSC (1991): Primary 04A20
- DOI: https://doi.org/10.1090/S0002-9939-99-04835-2
- MathSciNet review: 1600136