A note on strong compactness and resurrectibility

Arthur Apter

Fundamenta Mathematicae (2000)

  • Volume: 165, Issue: 3, page 258-290
  • ISSN: 0016-2736

Abstract

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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.

How to cite

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Apter, Arthur. "A note on strong compactness and resurrectibility." Fundamenta Mathematicae 165.3 (2000): 258-290. <http://eudml.org/doc/212470>.

@article{Apter2000,
abstract = {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.},
author = {Apter, Arthur},
journal = {Fundamenta Mathematicae},
keywords = {supercompact cardinal; strongly compact cardinal; indestructibility; resurrectibility; forcing},
language = {eng},
number = {3},
pages = {258-290},
title = {A note on strong compactness and resurrectibility},
url = {http://eudml.org/doc/212470},
volume = {165},
year = {2000},
}

TY - JOUR
AU - Apter, Arthur
TI - A note on strong compactness and resurrectibility
JO - Fundamenta Mathematicae
PY - 2000
VL - 165
IS - 3
SP - 258
EP - 290
AB - 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.
LA - eng
KW - supercompact cardinal; strongly compact cardinal; indestructibility; resurrectibility; forcing
UR - http://eudml.org/doc/212470
ER -

References

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  1. [1] A. Apter, Aspects of strong compactness, measurability, and indestructibility, Arch. Math. Logic, submitted. Zbl1024.03047
  2. [2] A. Apter, Laver indestructibility and the class of compact cardinals, J. Symbolic Logic 63 (1998) 149-157. Zbl0899.03038
  3. [3] A. Apter, Patterns of compact cardinals, Ann. Pure Appl. Logic 89 (1997), 101-115. Zbl0890.03026
  4. [4] A. Apter and M. Gitik, The least measurable can be strongly compact and indestructible, J. Symbolic Logic 63 (1998), 1404-1412. Zbl0926.03067
  5. [5] A. Apter and J. D. Hamkins, Universal indestructibility, Kobe J. Math. 16 (1999), 119-130. 
  6. [6] A. Apter and S. Shelah, Menas' result is best possible, Trans. Amer. Math. Soc. 349 (1997), 2007-2034. Zbl0876.03030
  7. [7] J. Cummings, A model in which GCH holds at successors but fails at limits, ibid. 329 (1992), 1-39. Zbl0758.03022
  8. [8] J. D. Hamkins, Destruction or preservation as you like it, Ann. Pure Appl. Logic 91 (1998), 191-229. Zbl0949.03047
  9. [9] J. D. Hamkins, Gap forcing, Israel J. Math., to appear. 
  10. [10] J. D. Hamkins, Gap forcing: generalizing the Lévy-Solovay theorem, Bull. Symbolic Logic 5 (1999), 264-272. Zbl0933.03067
  11. [11] J. D. Hamkins, Small forcing makes any cardinal superdestructible, J. Symbolic Logic 63 (1998), 51-58 Zbl0906.03051
  12. [12] J. D. Hamkins, The lottery preparation, Ann. Pure Appl. Logic 101 (2000), 103-146. Zbl0949.03045
  13. [13] R. Laver, Making the supercompactness of κ indestructible under κ -directed closed forcing, Israel J. Math. 29 (1978), 385-388. Zbl0381.03039
  14. [14] A. Lévy and R. Solovay, Measurable cardinals and the continuum hypothesis, ibid. 5 (1967), 234-248. Zbl0289.02044
  15. [15] T. Menas, On strong compactness and supercompactness, Ann. Math. Logic 7 (1974), 327-359. Zbl0299.02084

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