A Study on The Covering Lemmas

Abstract

The Covering Property is closely related to the existence of large core models and continues to be one of the most important driving forces of the fine structural inner model theory. This paper discusses the covering lemmas for L, Steel's core model K, the Dodd-Jensen core model K^DJ and L[U] in a sequencial order, and investigates the analogy and consistency between the different covering and weak covering proofs. Historical notes are included to help the readers understand the motivations of each idea and proof.