A note on strong compactness and resurrectibility
Apter, Arthur
Fundamenta Mathematicae, Tome 163 (2000), p. 258-290 / Harvested from The Polish Digital Mathematics Library
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We construct a model containing a proper class of strongly compact cardinals in which no strongly compact cardinal ĸ is ĸ+ supercompact and in which every strongly compact cardinal has its strong compactness resurrectible.

Publié le : 2000-01-01
EUDML-ID : urn:eudml:doc:212470 
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     pages = {258-290},
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Apter, Arthur. A note on strong compactness and resurrectibility. Fundamenta Mathematicae, Tome 163 (2000) pp. 258-290. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv165i3p258bwm/

[00000] [1] A. Apter, Aspects of strong compactness, measurability, and indestructibility, Arch. Math. Logic, submitted. | Zbl 1024.03047

[00001] [2] A. Apter, Laver indestructibility and the class of compact cardinals, J. Symbolic Logic 63 (1998) 149-157. | Zbl 0899.03038

[00002] [3] A. Apter, Patterns of compact cardinals, Ann. Pure Appl. Logic 89 (1997), 101-115. | Zbl 0890.03026

[00003] [4] A. Apter and M. Gitik, The least measurable can be strongly compact and indestructible, J. Symbolic Logic 63 (1998), 1404-1412. | Zbl 0926.03067

[00004] [5] A. Apter and J. D. Hamkins, Universal indestructibility, Kobe J. Math. 16 (1999), 119-130.

[00005] [6] A. Apter and S. Shelah, Menas' result is best possible, Trans. Amer. Math. Soc. 349 (1997), 2007-2034. | Zbl 0876.03030

[00006] [7] J. Cummings, A model in which GCH holds at successors but fails at limits, ibid. 329 (1992), 1-39. | Zbl 0758.03022

[00007] [8] J. D. Hamkins, Destruction or preservation as you like it, Ann. Pure Appl. Logic 91 (1998), 191-229. | Zbl 0949.03047

[00008] [9] J. D. Hamkins, Gap forcing, Israel J. Math., to appear.

[00009] [10] J. D. Hamkins, Gap forcing: generalizing the Lévy-Solovay theorem, Bull. Symbolic Logic 5 (1999), 264-272. | Zbl 0933.03067

[00010] [11] J. D. Hamkins, Small forcing makes any cardinal superdestructible, J. Symbolic Logic 63 (1998), 51-58 | Zbl 0906.03051

[00011] [12] J. D. Hamkins, The lottery preparation, Ann. Pure Appl. Logic 101 (2000), 103-146. | Zbl 0949.03045

[00012] [13] R. Laver, Making the supercompactness of κ indestructible under κ -directed closed forcing, Israel J. Math. 29 (1978), 385-388. | Zbl 0381.03039

[00013] [14] A. Lévy and R. Solovay, Measurable cardinals and the continuum hypothesis, ibid. 5 (1967), 234-248. | Zbl 0289.02044

[00014] [15] T. Menas, On strong compactness and supercompactness, Ann. Math. Logic 7 (1974), 327-359. | Zbl 0299.02084