33 research outputs found
Indiscernible Sequences for Extenders, and the Singular Cardinal Hypothesis
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 is a singular strong limit cardinal and where is not the successor of a cardinal of cofinality at
most .
(i) If \cofinality(\kappa)>\gw then .
(ii) If \cofinality(\kappa)=\gw then either or
\set{\ga:K\sat o(\ga)\ge\ga^{+n}} is cofinal in 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