Chang's model and covering properties (Q1119631)

The author studies the covering properties of the Chang model C (the equivalent of the constructible universe for the infinitary language \({\mathcal L}_{\omega_ 1,\omega_ 1})\) and of the model \(N=\cup \{L(A)\); A countable set of ordinals\(\}\). She shows, e.g., that the failure of the covering property for C is equiconsistent with the existence of uncountably many measurable cardinals. A similar result is obtained for the model N. The main tool used in the paper are the core model techniques.