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Indiscernible Sequences for Extenders, and the Singular Cardinal Hypothesis by Gitik, Moti; Mitchell, William is a scholarly article available to read on EtoBox.

What is Indiscernible Sequences for Extenders, and the Singular Cardinal Hypothesis about?

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 $\kappa$ is a singular strong limit cardinal and $2^\kappa >= \lambda$ where $\lambda$ is not the successor of a cardinal of cofinality at most $\kappa$. (i) If $\cofinality(\kappa)>\gw$ then $o(\kappa)\ge\lambda$. (ii) If $\cofinality(\kappa)=\gw$ then either $o(\kappa)\ge\lambda$ or $\set{\ga:K\sat o(\ga)\ge\ga^{+n}}$ is cofinal in $\kappa$ for each $n\in\gw$. In order to prove this theorem we give a detailed analysis of the sequences of indiscernibles which come from applying the covering lemma to nonoverlapping sequences of extenders.

Author

Gitik, Moti; Mitchell, William

Published

1995

Language

EN