Notre Dame Journal of Formal Logic

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

P. D. Welch

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.

Article information

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

Dates
First available in Project Euclid: 30 August 2005

Permanent link to this document
http://projecteuclid.org/euclid.ndjfl/1125409336

Digital Object Identifier
doi:10.1305/ndjfl/1125409336

Mathematical Reviews number (MathSciNet)
MR2162108

Subjects
Primary: 03E55: Large cardinals 03E45: Inner models, including constructibility, ordinal definability, and core models 03E10: Ordinal and cardinal numbers 03E04: Ordered sets and their cofinalities; pcf theory

Keywords
large cardinals constructibility cofinality mutual stationarity measurable cardinals

Citation

Welch, P. D. Some Open Problems in Mutual Stationarity Involving Inner Model Theory: A Commentary. Notre Dame J. Formal Logic 46 (2005), no. 3, 375--379. doi:10.1305/ndjfl/1125409336. http://projecteuclid.org/euclid.ndjfl/1125409336.


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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.
  • [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.
  • [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.