Abstract
We prove an indestructibility theorem for degrees of supercompactness that is compatible with level by level equivalence between strong compactness and supercompactness.
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Apter A.: Diamond, square, and level by level equivalence. Arch. Math. Logic 44, 387–395 (2005)
Apter A.: Failures of GCH and the level by level equivalence between strong compactness and supercompactness. Math. Logic Q. 49, 587–597 (2003)
Apter A.: Indestructibility, strongness, and level by level equivalence. Fundam. Math. 177, 45–54 (2003)
Apter A.: Indestructibility under adding Cohen subsets and level by level equivalence. Math. Logic Q. 55, 271–279 (2009)
Apter A.: More Easton theorems for level by level equivalence. Colloq. Math. 128, 69–86 (2012)
Apter A.: Supercompactness and level by level equivalence are compatible with indestructibility for strong compactness. Arch. Math. Logic 46, 155–163 (2007)
Apter A.: Supercompactness and measurable limits of strong cardinals II: Applications to level by level equivalence. Math. Logic Q. 52, 457–463 (2006)
Apter A., Hamkins J.D.: Indestructibility and the level-by-level agreement between strong compactness and supercompactness. J. Symb. Logic 67, 820–840 (2002)
Apter A., Hamkins J.D.: Universal indestructibility. Kobe J. Math. 16, 119–130 (1999)
Apter A., Shelah S.: On the strong equality between supercompactness and strong compactness. Trans. Am. Math. Soc. 349, 103–128 (1997)
Hamkins J.D.: Gap forcing. Isr. J. Math. 125, 237–252 (2001)
Hamkins J.D.: Gap forcing: Generalizing the Lévy–Solovay Theorem. Bull. Symb. Logic 5, 264–272 (1999)
Hamkins J.D.: The lottery preparation. Ann. Pure Appl. Logic 101, 103–146 (2000)
Hamkins J.D.: Small forcing makes any cardinal superdestructible. J. Symb. Logic 63, 51–58 (1998)
Jech T.: Set Theory: The Third Millennium Edition, Revised and Expanded. Springer, Berlin (2003)
Laver R.: Making the supercompactness of κ indestructible under κ-directed closed forcing. Isr. J. Math. 29, 385–388 (1978)
Magidor M.: On the existence of nonregular ultrafilters and the cardinality of ultrapowers. Trans. Am. Math. Soc. 249, 97–111 (1979)
Menas, T.: On strong compactness and supercompactness. Ann. Math. Logic 7, 327–359 (1974/75)
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The author’s research was partially supported by PSC-CUNY grants.
The author would like to thank the referee for helpful comments and suggestions which have been incorporated into the current version of the paper.
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Apter, A.W. A universal indestructibility theorem compatible with level by level equivalence. Arch. Math. Logic 54, 463–470 (2015). https://doi.org/10.1007/s00153-015-0421-3
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DOI: https://doi.org/10.1007/s00153-015-0421-3
Keywords
- Supercompact cardinal
- Level by level equivalence between strong compactness and supercompactness
- Indestructibility
- Lottery sum