### Some Open Problems in Mutual Stationarity Involving Inner Model Theory: A Commentary

P. D. Welch
Source: Notre Dame J. Formal Logic Volume 46, Number 3 (2005), 375-379.

#### Abstract

We discuss some of the relationships between the notion of "mutual stationarity" of Foreman and Magidor and measurability in inner models. The general thrust of these is that very general mutual stationarity properties on small cardinals, such as the ℵns, is a large cardinal property. A number of open problems, theorems, and conjectures are stated.

First Page:
Primary Subjects: 03E55, 03E45, 03E10, 03E04
Full-text: Open access

Permanent link to this document: http://projecteuclid.org/euclid.ndjfl/1125409336
Digital Object Identifier: doi:10.1305/ndjfl/1125409336
Mathematical Reviews number (MathSciNet): MR2162108

### References

[1] Cummings, J., M. Foreman, and M. Magidor, "Canonical structure in the universe of set theory. II", forthcoming in Annals of Pure and Applied Logic.
Mathematical Reviews (MathSciNet): MR1838355
Digital Object Identifier: doi:10.1142/S021906130100003X
Zentralblatt MATH: 0988.03075
[2] Foreman, M., and M. Magidor, "Mutually stationary sequences of sets and the non-saturation of the non-stationary ideal on $P\sb \varkappa(\lambda)$", Acta Mathematica, vol. 186 (2001), pp. 271--300.
Mathematical Reviews (MathSciNet): MR2002g:03094
Zentralblatt MATH: 1017.03022
[3] Koepke, P., and P. D. Welch, "Mutual stationarity: Measures of higher Mitchell order", in preparation.
[4] Koepke, P., and P. D. Welch, "On the strength of mutual stationarity", forthcoming in Proceedings of the Set Theory Year, CRM Barcelona, edited by J. Bagaria, Birkäuser Press.
[5] Zeman, M., Inner Models and Large Cardinals, vol. 5 of de Gruyter Series in Logic and Its Applications, Walter de Gruyter & Co., Berlin, 2002.
Mathematical Reviews (MathSciNet): MR2003a:03004
Zentralblatt MATH: 0987.03002