The sharp for the Chang model is small

Abstract

Woodin has shown that if there is a measurable Woodin cardinal then there is, in an appropriate sense, a sharp for the Chang model. We produce, in a weaker sense, a sharp for the Chang model using only the existence of a cardinal $\kappa$ having an extender of length ${\kappa }^{+{\omega }_1}$.

To appear in the Archive for Mathematical Logic