Indiscernible Sequences for Extenders, and the Singular Cardinal Hypothesis [article]

Moti Gitik, William Mitchell
1995 arXiv   pre-print
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 2^κ >= λ where λ is not the successor of a cardinal of cofinality at most κ. (i) If (κ)> then o(κ)>λ. (ii) If (κ)= then either o(κ)>λ or :K o()>^+n is cofinal in κ for each n∈. In order to prove this theorem we give a detailed analysis of the sequences of indiscernibles
more » ... hich come from applying the covering lemma to nonoverlapping sequences of extenders.
arXiv:math/9507214v1 fatcat:r5mqjv5l5jguvhpehzoqpnmwbi