IJPAM: Volume 68, No. 4 (2011)

NORMAL ULTRAFILTERS AND MAHLO RANK

Martin Dowd
1613, Wintergreen Pl.
Costa Mesa, CA 92626, USA
e-mail: [email protected]


Abstract. It is straightforward that, if GCH holds then the Mahlo rank of an inaccessible cardinal $\kappa$ is less than $\kappa^{++}$. If it could be shown that the Mitchell order of a measurable cardinal is at most its Mahlo rank, it would follow that the Mitchell order is less than $\kappa^{++}$. It is shown that the Mitchell order is at most the Mahlo rank, if the Mitchell order is less than ${\kappa^+}^{\omega}$.

Received: March 1, 2011

AMS Subject Classification: 03E55

Key Words and Phrases: Mitchell order, stationary reflection order

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 68
Issue: 4