The indescribability of the order of the indescribable cardinals

Annals of Pure and Applied Logic 57 (1):45-91 (1992)
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Abstract

We prove the following consistency results about indescribable cardinals which answer a question of A. Kanamori and M. Magidor .Theorem 1.1 . CON.Theorem 5.1 . Assuming the existence of σmn indescribable cardinals for all m < ω and n < ω and given a function : {: m 2, n } 1} → {0,1} there is a poset P L[] such that GCH holds in P and Theorem 1.1 extends the work begun in [2], and its proof uses an iterated forcing construction together with master condition arguments. By combining these techniques with some observations about small forcing and indescribability, one obtains the Easton-style result 5.1

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Indescribable cardinals without diamonds.Kai Hauser - 1992 - Archive for Mathematical Logic 31 (5):373-383.

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Indescribable cardinals and elementary embeddings.Kai Hauser - 1991 - Journal of Symbolic Logic 56 (2):439-457.

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