Inner model theory

Inner model theory is the study of the "fine structure theory" and construction of inner models, proper class-sized models of ZFC which satisfy the existence of large cardinals, covering, the generalized continuum hypothesis, and more. The smallest inner model is \(L\), which arguably has the most and the most detailed fine structure, but it is unable to accommodate measurable cardinals, in the sense that no cardinal, even if it really is measurable, is measurable in \(L\), and thus one needs to find inner models larger than \(L\).

Inner model theory has given rise to the study of sharps, and many new large cardinal axioms were developed for the purpose of inner model theory.