Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



$ I[\omega_2]$ can be the nonstationary ideal on $ \operatorname{Cof}(\omega_1)$

Author: William J. Mitchell
Journal: Trans. Amer. Math. Soc. 361 (2009), 561-601
MSC (2000): Primary 03E35
Published electronically: September 8, 2008
MathSciNet review: 2452816
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Abstract: We answer a question of Shelah by showing that it is consistent that every member of $ I[\omega_2]\cap\operatorname{Cof}(\omega_1)$ is nonstationary if and only if it is consistent that there is a $ \kappa^+$-Mahlo cardinal $ \kappa$.

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Additional Information

William J. Mitchell
Affiliation: Department of Mathematics, University of Florida, P.O. Box 118105, Gainesville, Florida 32611-8105

Received by editor(s): September 5, 2005
Published electronically: September 8, 2008
Additional Notes: The author would like to thank Matt Foreman, Bernard Koenig and the referee of this paper for valuable remarks and corrections. In addition the author would like to thank Matt Foremann and Martin Zeman for inviting him to the University of California at Irvine for a week during which he gave an extended exposition of this work. Suggestions made during this visit led directly to a dramatically improved revision of this paper. \endgraf The writing of this paper was partially supported by grant number DMS-0400954 from the National Science Foundation.
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