Gap forcing: generalizing the Levy-Solovay theorem

Details Gap forcing: generalizing the Levy-Solovay theorem Gap forcing: generalizing the Levy-Solovay theorem

1999-01-25

arxiv.org/abs/math/9901108v1

Mathematics

Logic

10 pages. The full technical details of the theorem announced in the this paper can be found in math.LO/9808011. The author's

Scientific paper

The landmark Levy-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.

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