Notre Dame Journal of Formal Logic

Many Normal Measures

Shimon Garti

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We characterize the situation of having at least (2κ)+-many normal ultrafilters on a measurable cardinal κ. We also show that if κ is a compact cardinal, then κ carries (2κ)+-many κ-complete ultrafilters, each of which extends the club filter on κ.

Article information

Notre Dame J. Formal Logic, Volume 55, Number 3 (2014), 349-357.

First available in Project Euclid: 22 July 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03E05: Other combinatorial set theory
Secondary: 03E55: Large cardinals

compact cardinal measurable cardinal normal measure club filter


Garti, Shimon. Many Normal Measures. Notre Dame J. Formal Logic 55 (2014), no. 3, 349--357. doi:10.1215/00294527-2688060.

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  • [1] Apter, A. W., J. Cummings, and J. D. Hamkins, “Large cardinals with few measures,” Proceedings of the American Mathematical Society, vol. 135 (2007), pp. 2291–2300.
  • [2] Baldwin, S., “The $\triangleleft$-ordering on normal ultrafilters,” Journal of Symbolic Logic, vol. 50 (1985), pp. 936–52.
  • [3] Friedman, S.-D., and M. Magidor, “The number of normal measures,” Journal of Symbolic Logic, vol. 74 (2009), pp. 1069–80.
  • [4] Jech, T., Set Theory, 3rd millennium ed., revised and expanded, Springer Monographs in Mathematics, Springer, Berlin, 2003.
  • [5] Kanamori, A., The Higher Infinite: Large Cardinals in Set Theory from Their Beginnings, 2nd ed., Springer Monographs in Mathematics, Springer, Berlin, 2003.
  • [6] Keisler, H. J., and A. Tarski, “From accessible to inaccessible cardinals: Results holding for all accessible cardinal numbers and the problem of their extension to inaccessible ones,” Fundamenta Mathematicae, vol. 53 (1963/1964), pp. 225–308.
  • [7] Kunen, K., “Some applications of iterated ultrapowers in set theory,” Annals of Mathematical Logic, vol. 1 (1970), pp. 179–227.
  • [8] Kunen, K., Set Theory: An Introduction to Independence Proofs, vol. 102 of Studies in Logic and the Foundations of Mathematics, North-Holland, Amsterdam, 1980.
  • [9] Kunen, K., and J. B. Paris, “Boolean extensions and measurable cardinals,” Annals of Mathematical Logic, vol. 2 (1970/1971), pp. 359–77.
  • [10] Magidor, M., “There are many normal ultrafiltres corresponding to a supercompact cardinal,” Israel Journal of Mathematics, vol. 9 (1971), pp. 186–92.
  • [11] Magidor, M., “How large is the first strongly compact cardinal? or A study on identity crises,” Annals of Mathematical Logic, vol. 10 (1976), pp. 33–57.
  • [12] Mitchell, W. J., “Sets constructible from sequences of ultrafilters,” Journal of Symbolic Logic, vol. 39 (1974), pp. 57–66.
  • [13] Solovay, R. M., “Real-valued measurable cardinals,” pp. 397–428 in Axiomatic Set Theory (Los Angeles, 1967), vol. 13 of Proceedings of Symposia in Pure Mathematics, American Mathematical Society, Providence, 1971.
  • [14] Vopěnka, P., and K. Hrbáček, “On strongly measurable cardinals,” Bulletin de l’Académie des Sciences, Serie des Sciences Mathematiques, vol. 14 (1966), pp. 587–91.