Annals of Pure and Applied Logic 101 (2-3):103-146 (2000)

Joel David Hamkins
Oxford University
The lottery preparation, a new general kind of Laver preparation, works uniformly with supercompact cardinals, strongly compact cardinals, strong cardinals, measurable cardinals, or what have you. And like the Laver preparation, the lottery preparation makes these cardinals indestructible by various kinds of further forcing. A supercompact cardinal κ, for example, becomes fully indestructible by <κ-directed closed forcing; a strong cardinal κ becomes indestructible by κ-strategically closed forcing; and a strongly compact cardinal κ becomes indestructible by, among others, the forcing to add a Cohen subset to κ, the forcing to shoot a club Cκ avoiding the measurable cardinals and the forcing to add various long Prikry sequences. The lottery preparation works best when performed after fast function forcing, which adds a new completely general kind of Laver function for any large cardinal, thereby freeing the Laver function concept from the supercompact cardinal context
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DOI 10.1016/s0168-0072(99)00010-x
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References found in this work BETA

Gap Forcing: Generalizing the Lévy-Solovay Theorem.Joel David Hamkins - 1999 - Bulletin of Symbolic Logic 5 (2):264-272.
On Strong Compactness and Supercompactness.Telis K. Menas - 1975 - Annals of Mathematical Logic 7 (4):327-359.
Destruction or Preservation as You Like It.Joel David Hamkins - 1998 - Annals of Pure and Applied Logic 91 (2-3):191-229.

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Citations of this work BETA

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Tall Cardinals.Joel D. Hamkins - 2009 - Mathematical Logic Quarterly 55 (1):68-86.

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