Applications of the covering lemma for sequences of measures

Mitchell, W.

doi:10.1090/S0002-9947-1987-0869398-2

Applications of the covering lemma for sequences of measures
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by W. Mitchell

Trans. Amer. Math. Soc. 299 (1987), 41-58

DOI: https://doi.org/10.1090/S0002-9947-1987-0869398-2

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Abstract:

We present several applications of the covering lemma for the core model for sequences of measures, including characterizations of the large cardinal strength necessary to make the filter of closed, unbounded subsets of ${\omega _1}$ an ultrafilter or to change the cofinality of a regular cardinal, and a characterization of the minimal inner model containing an arbitrary elementary embedding.

References

A. Dodd and R. Jensen, The core model, Ann. Math. Logic 20 (1981), no. 1, 43–75. MR 611394, DOI 10.1016/0003-4843(81)90011-5
Tony Dodd and Ronald Jensen, The covering lemma for $K$, Ann. Math. Logic 22 (1982), no. 1, 1–30. MR 661475, DOI 10.1016/0003-4843(82)90013-4
Tony Dodd and Ronald Jensen, The covering lemma for $K$, Ann. Math. Logic 22 (1982), no. 1, 1–30. MR 661475, DOI 10.1016/0003-4843(82)90013-4
K. Kunen and J. B. Paris, Boolean extensions and measurable cardinals, Ann. Math. Logic 2 (1970/71), no. 4, 359–377. MR 277381, DOI 10.1016/0003-4843(71)90001-5
Menachem Magidor, Changing cofinality of cardinals, Fund. Math. 99 (1978), no. 1, 61–71. MR 465868, DOI 10.4064/fm-99-1-61-71
William J. Mitchell, Sets constructible from sequences of ultrafilters, J. Symbolic Logic 39 (1974), 57–66. MR 344123, DOI 10.2307/2272343
William Mitchell, How weak is a closed unbounded ultrafilter?, Logic Colloquium ’80 (Prague, 1980) Studies in Logic and the Foundations of Mathematics, vol. 108, North-Holland, Amsterdam-New York, 1982, pp. 209–230. MR 673794
William J. Mitchell, The core model for sequences of measures. I, Math. Proc. Cambridge Philos. Soc. 95 (1984), no. 2, 229–260. MR 735366, DOI 10.1017/S030500410006151X

Indiscernibles, skies and ultrafilters

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The core model for sequences of measures

K. L. Prikry, Changing measurable into accessible cardinals, Dissertationes Math. (Rozprawy Mat.) 68 (1970), 55. MR 262075