Indiscernible sequences for extenders, and the singular cardinal hypothesis

Moti Gitik, William J. Mitchell

Research output: Contribution to journalArticlepeer-review

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 K is a singular strong limit cardinal and 2K ≥ λ where λ is not the successor of a cardinal of cofinality at most K. If cf(K) > ω then it follows that ο(K) ≥ λ, and if cf(K) = ω then either ο(K) ≥ λ or {α : Κ l= ο(α)≥α+n} is confinal in K for each n ∈ ω. We also prove several results which extend or are related to this result, notably Theorem. If 2ω < Nω and 2Nω > Nω1 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.

Original languageEnglish
Pages (from-to)273-316
Number of pages44
JournalAnnals of Pure and Applied Logic
Volume82
Issue number3
DOIs
StatePublished - 15 Dec 1996

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