A note on strong compactness and resurrectibility

• Autorzy: Arthur W. Apter
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

supercompact cardinal; strongly compact cardinal; indestructibility; resurrectibility

Kategorie tematyczne

• 03E55: Large cardinals
• 03E35: Consistency and independence results

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2000
• Tom: 165
• Numer: 3
• Strony: 258-290

Daty

wydano

2000

otrzymano

2000-02-01

Twórcy

autor

Arthur W. Apter

• Department of Mathematics, Baruch College of CUNY, New York, NY 10010, U.S.A.

Bibliografia

• [1] A. Apter, Aspects of strong compactness, measurability, and indestructibility, Arch. Math. Logic, submitted.
• [2] A. Apter, Laver indestructibility and the class of compact cardinals, J. Symbolic Logic 63 (1998) 149-157.
• [3] A. Apter, Patterns of compact cardinals, Ann. Pure Appl. Logic 89 (1997), 101-115.
• [4] A. Apter and M. Gitik, The least measurable can be strongly compact and indestructible, J. Symbolic Logic 63 (1998), 1404-1412.
• [5] A. Apter and J. D. Hamkins, Universal indestructibility, Kobe J. Math. 16 (1999), 119-130.
• [6] A. Apter and S. Shelah, Menas' result is best possible, Trans. Amer. Math. Soc. 349 (1997), 2007-2034.
• [7] J. Cummings, A model in which GCH holds at successors but fails at limits, ibid. 329 (1992), 1-39.
• [8] J. D. Hamkins, Destruction or preservation as you like it, Ann. Pure Appl. Logic 91 (1998), 191-229.
• [9] J. D. Hamkins, Gap forcing, Israel J. Math., to appear.
• [10] J. D. Hamkins, Gap forcing: generalizing the Lévy-Solovay theorem, Bull. Symbolic Logic 5 (1999), 264-272.
• [11] J. D. Hamkins, Small forcing makes any cardinal superdestructible, J. Symbolic Logic 63 (1998), 51-58
• [12] J. D. Hamkins, The lottery preparation, Ann. Pure Appl. Logic 101 (2000), 103-146.
• [13] R. Laver, Making the supercompactness of κ indestructible under κ -directed closed forcing, Israel J. Math. 29 (1978), 385-388.
• [14] A. Lévy and R. Solovay, Measurable cardinals and the continuum hypothesis, ibid. 5 (1967), 234-248.
• [15] T. Menas, On strong compactness and supercompactness, Ann. Math. Logic 7 (1974), 327-359.