Gap forcing: Generalizing the lévy-Solovay theorem

Bulletin of Symbolic Logic 5 (2):264-272 (1999)

Authors
Joel David Hamkins
Oxford University
Abstract
The Lévy-Solovay Theorem [8] 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
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DOI 10.2307/421092
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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.
Small Forcing Makes Any Cardinal Superdestructible.Joel Hamkins - 1998 - Journal of Symbolic Logic 63 (1):51-58.
Canonical Seeds and Prikry Trees.Joel Hamkins - 1997 - Journal of Symbolic Logic 62 (2):373-396.

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