Bulletin of Symbolic Logic 5 (2):264-272 (1999)
The Lévy-Solovay Theorem  limits the kind of large cardinal embeddings that can exist in a small forcing extension. Here I announce a generalization of this theorem to a broad new class of forcing notions. One consequence is that many of the forcing iterations most commonly found in the large cardinal literature create no new weakly compact cardinals, measurable cardinals, strong cardinals, Woodin cardinals, strongly compact cardinals, supercompact cardinals, almost huge cardinals, huge cardinals, and so on
|Keywords||No keywords specified (fix it)|
|Categories||categorize this paper)|
References found in this work BETA
Destruction or Preservation as You Like It.Joel David Hamkins - 1998 - Annals of Pure and Applied Logic 91 (2-3):191-229.
Citations of this work BETA
The Lottery Preparation.Joel David Hamkins - 2000 - Annals of Pure and Applied Logic 101 (2-3):103-146.
Large Cardinals and Definable Well-Orders on the Universe.Andrew D. Brooke-Taylor - 2009 - Journal of Symbolic Logic 74 (2):641-654.
Coding Into HOD Via Normal Measures with Some Applications.Arthur W. Apter & Shoshana Friedman - 2011 - Mathematical Logic Quarterly 57 (4):366-372.
Indestructible Strong Compactness and Level by Level Inequivalence.Arthur W. Apter - 2013 - Mathematical Logic Quarterly 59 (4-5):371-377.
Tallness and Level by Level Equivalence and Inequivalence.Arthur W. Apter - 2010 - Mathematical Logic Quarterly 56 (1):4-12.
Similar books and articles
Solovay Models and Forcing Extensions.Joan Bagaria & Roger Bosch - 2004 - Journal of Symbolic Logic 69 (3):742-766.
Proper Forcing and L(ℝ).Itay Neeman & Jindřich Zapletal - 2001 - Journal of Symbolic Logic 66 (2):801-810.
Small Forcing Makes Any Cardinal Superdestructible.Joel David Hamkins - 1998 - Journal of Symbolic Logic 63 (1):51-58.
Some Structural Results Concerning Supercompact Cardinals.Arthur W. Apter - 2001 - Journal of Symbolic Logic 66 (4):1919-1927.
Unfoldable Cardinals and the GCH.Joel David Hamkins - 2001 - Journal of Symbolic Logic 66 (3):1186-1198.
On Measurable Limits of Compact Cardinals.Arthur W. Apter - 1999 - Journal of Symbolic Logic 64 (4):1675-1688.
Co-Stationarity of the Ground Model.Natasha Dobrinen & Sy-David Friedman - 2006 - Journal of Symbolic Logic 71 (3):1029 - 1043.
Laver Indestructibility and the Class of Compact Cardinals.Arthur W. Apter - 1998 - Journal of Symbolic Logic 63 (1):149-157.
Exactly Controlling the Non-Supercompact Strongly Compact Cardinals.Arthur W. Apter & Joel David Hamkins - 2003 - Journal of Symbolic Logic 68 (2):669-688.
Added to index2009-01-28
Total downloads164 ( #28,588 of 2,177,875 )
Recent downloads (6 months)1 ( #317,247 of 2,177,875 )
How can I increase my downloads?