Indiscernible sequences for extenders, and the singular cardinal hypothesis

Annals of Pure and Applied Logic 82 (3):273-316 (1996)
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Abstract

We prove several results giving lower bounds for the large cardinal strength of a failure of the singular cardinal hypothesis. The main result is the following theorem: Theorem. Suppose κ is a singular strong limit cardinal and 2κ λ where λ is not the successor of a cardinal of cofinality at most κ. If cf > ω then it follows that o λ, and if cf = ωthen either o λ or {α: K o α+n} is confinal in κ for each n ε ω.We also prove several results which extend or are related to this result, notably Theorem. If 2ω ω1 then there is a sharp for a model with a strong cardinal.In order to prove these theorems we give a detailed analysis of the sequences of indiscernibles which come from applying the covering lemma to nonoverlapping sequences of extenders

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Citations of this work

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References found in this work

The core model.A. Dodd & R. Jensen - 1981 - Annals of Mathematical Logic 20 (1):43-75.
The negation of the singular cardinal hypothesis from o(K)=K++.Moti Gitik - 1989 - Annals of Pure and Applied Logic 43 (3):209-234.
The covering lemma for K.Tony Dodd & Ronald Jensen - 1982 - Annals of Mathematical Logic 22 (1):1-30.
The strenght of the failure of the singular cardinal hypothesis.Moti Gitik - 1991 - Annals of Pure and Applied Logic 51 (3):215-240.

View all 10 references / Add more references