Core model

Summary

A core model is an inner model, usually written $K$, built from fine-structural pieces like the constructible universe. Unlike $L$, it is large enough to contain some large cardinal structure. It is defined under an assumption that rules out large cardinals beyond a certain level. An example of such an assumption is that there is no inner model with a Woodin cardinal. Under such an assumption the core model is close to the universe $V$, in the sense of covering properties like Jensen's covering theorem for $L$. The theory of the core model links large cardinals with the strength of combinatorial statements.